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time-frequency analysis | Short Time Fourier Transform analysis of newborn baby cry signal | https://dsp.stackexchange.com/questions/22558/short-time-fourier-transform-analysis-of-newborn-baby-cry-signal | <p>I am working on analysis of baby cry signal. fundamental frequency(Fo) of signal is already estimated using auto correlation and cepstrum analysis. cry signal is inputted in .wav format. now i want to do short time fourier transform analysis of same signal inorder to find variations in fundamental frequency over the... | <p>Have a look at <a href="http://labrosa.ee.columbia.edu/projects/SAcC/" rel="nofollow">SAaC</a> from <a href="http://labrosa.ee.columbia.edu/" rel="nofollow">LabROSA</a>. You also might be interested in <a href="https://github.com/dpwe/pitchflow" rel="nofollow">delta pitch without explicit pitch tracking</a>.</p>
| 1,034 |
time-frequency analysis | A mathematical justification of discontinuity detection using STFT | https://dsp.stackexchange.com/questions/86782/a-mathematical-justification-of-discontinuity-detection-using-stft | <p>I'm trying to detect rapid changes in a one-dimensional signal say <span class="math-container">$[0,1]\ni t \mapsto f(t) \in [-1,1]$</span>. By rapid changes, I mean corner points, edges, or sharp transitions at a point for example the signal switches from a value <span class="math-container">$-1$</span> to <span cl... | 1,035 | |
time-frequency analysis | Isolating frequency-specific oscillation from transient | https://dsp.stackexchange.com/questions/49229/isolating-frequency-specific-oscillation-from-transient | <p>I am performing time-frequency analysis on electrophysiological data with complex morlet wavelets. Each decomposition in the attached figure shows <em>total power</em> following the onset of a stimulus (top row) or preceding an eye movement (bottom row). There is a broadband, transient increase in power following st... | <p>The notation and terminology in this and the <a href="http://www.fil.ion.ucl.ac.uk/~karl/A%20neural%20mass%20model%20for%20MEG.pdf" rel="nofollow noreferrer">closely related paper</a> could have been more simplified I think.</p>
<p>To understand what's going on there, we need to start from page 1583. Specifically:<... | 1,036 |
time-frequency analysis | Conditions for symmetric and unimodal windows in both time and frequency domains | https://dsp.stackexchange.com/questions/36247/conditions-for-symmetric-and-unimodal-windows-in-both-time-and-frequency-domains | <p>After a lecture on harmonic analysis and time/frequency methods, I reconsidered the Gaussian kernel, defined in continuous time. </p>
<p>It is unimodal and symmetric, and its continuous Fourier transform is another Gaussian, thus unimodal and symmetric (from <a href="https://stackoverflow.com/questions/5398304/four... | <p>This is only also partial answer. I translate unimodular into ripple-free, because ripples are essentially extremal points, and we just want to have a single one.</p>
<p>A ripple-free Fourier Transform translates (to my knowledge) to an infinitely often continuously differentiable time-domain function. Furthermore,... | 1,037 |
time-frequency analysis | Trying to understand WAVELET TRANSFORM Frequncy-Time diagram | https://dsp.stackexchange.com/questions/9319/trying-to-understand-wavelet-transform-frequncy-time-diagram | <p>I am reading </p>
<p><a href="http://users.rowan.edu/~polikar/WAVELETS/WTpart3.html" rel="nofollow noreferrer">The Wavelet Tutorial</a></p>
<p>Part III
MULTIRESOLUTION ANALYSIS
&
THE CONTINUOUS WAVELET TRANSFORM</p>
<p>by
Robi Polikar </p>
<p>The author explains about the following fig and says;</p>
<blockq... | <p>I believe by the WT, you are talking about the discrete wavelet transform, DWT.</p>
<p>This can be thought of as a subsampling of the continuous wavelet transform, CWT. In the case of the DWT, we pick frequencies of the form $2^{j-1}$ for ($j=1,2,\dots$) and then pick times seperated by multiples of $2^j$.</p>
<p>... | 1,038 |
time-frequency analysis | Is it a good idea to start with wavelet theory before reading recent spectrum sensing papers? | https://dsp.stackexchange.com/questions/96565/is-it-a-good-idea-to-start-with-wavelet-theory-before-reading-recent-spectrum-se | <p>my research focuses on wideband spectrum sensing. I'm currently reading <strong>"A Wavelet Tour of Signal Processing" by Stéphane Mallat</strong>, and I find it very rich and foundational.</p>
<p>My current approach is to:</p>
<p>Read Mallat’s book carefully to understand wavelet theory, time-frequency ana... | <p>Considering your very fundamental newer question, <a href="https://dsp.stackexchange.com/questions/96567/what-makes-wavelet-coefficients-large-similarity-with-the-wavelet-shape-or-sig/96575#96575">What makes wavelet coefficients large — similarity with the wavelet shape or signal irregularities?</a> , I'd say it's c... | 1,039 |
time-frequency analysis | scipy.signal.spectrogram | https://dsp.stackexchange.com/questions/46516/scipy-signal-spectrogram | <p>I want to do time-frequency analysis of a signal. So i decided to use <a href="https://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.signal.spectrogram.html" rel="nofollow noreferrer">spectrogram</a> function from scipy. This function returns, three parameters f,t,Sxx. I am using below arguements:</p>
<... | <p>As the returned value shows, the first spectrum is computed at time $t=0.15$ s. With a sampling rate of 1000 Hz, that means that the first analysis window is centred at sample $n=150$. So the first analysis frame spans the samples $n \in [0,300[$. </p>
<p>Because your overlap is set to 25 samples, the second analys... | 1,040 |
time-frequency analysis | Extract frequency data from MP3 file | https://dsp.stackexchange.com/questions/58403/extract-frequency-data-from-mp3-file | <p>I want to do frequency analysis of audio data, basically trying to figure out what the notes are in a song algorithmically. The standard approach is to decode the MP3 into PCM data and run it through an FFT. However, notes below around middle C require too much precision for an FFT to work well. Since the MP3 alr... | <p>The MP3 encoder works on batches of 576 time-domain samples and converts them to 576 frequency-domain samples. That means that you get a frequency resolution of <span class="math-container">$\frac{f_\text{sample}}{576}$</span>, whatever your sampling rate is.</p>
<p>Notice however how short that is at usual samplin... | 1,041 |
time-frequency analysis | Does Wigner-Ville distribution provide the highest resolution? | https://dsp.stackexchange.com/questions/17058/does-wigner-ville-distribution-provide-the-highest-resolution | <p>For linear time-frequency representation, the resolution is limited by <a href="https://en.wikipedia.org/wiki/Gabor_limit#Signal_processing" rel="noreferrer">Gabor limit</a>. However, if interference is allowed, the resolution may be higher. What is the possible resolution in such a case? In "Electroencephalography ... | <p>The statement is true if you restrict it to all TF distributions in the <a href="http://en.wikipedia.org/wiki/Bilinear_time%E2%80%93frequency_distribution" rel="nofollow">Cohen Class</a>. That is rather easy to see, because the Wigner distribution generates all other distribution in that class by convolution with a ... | 1,042 |
time-frequency analysis | The separation condition of a multi-component signal | https://dsp.stackexchange.com/questions/81169/the-separation-condition-of-a-multi-component-signal | <p>Suppose a signal is a superposition of multiple intrinsic-mode-type (IMT)
functions, say
<span class="math-container">$$f(t) = \sum_{i=1}^n A_i(t)e^{i\varphi_i(t)} $$</span>
Why is the separation condition of <span class="math-container">$f(t)$</span> be
<span class="math-container">$$\forall i,j \quad|\varphi_i^\pr... | <blockquote>
<p>why the peak of the ridge can represent the instantaneous frequency.</p>
</blockquote>
<p>The idea is that the peak in the frequency domain is the "frequency" of the signal. So if the frequency changes, the peak should move to be centered at the new frequency.</p>
<blockquote>
<p>Also, is ther... | 1,043 |
time-frequency analysis | Defining an average in time for a density in time | https://dsp.stackexchange.com/questions/24904/defining-an-average-in-time-for-a-density-in-time | <p>I'm reading the text book "Time-Frequency Analysis" by Leon Cohen and I've made my way through a decent portion. There is however a conceptual issue I keep coming back to. The book states:</p>
<blockquote>
<p>If we consider $\lvert s(t)\rvert^2$ as a density in time, the average
time can be defined in the usual... | <p>Take a signal defined on the real line, defined by the time location <span class="math-container">$t$</span>. Weight them locally at time <span class="math-container">$t$</span> by the energy of the signal, or squared magnitude <span class="math-container">$s|(t)|^2$</span>. A definition of <strong>some average time... | 1,044 |
time-frequency analysis | Need to learn wavelet, suggest steps and resources | https://dsp.stackexchange.com/questions/14109/need-to-learn-wavelet-suggest-steps-and-resources | <p>I am looking for a good introduction to wavelets and wavelet transforms.</p>
<p>that covers the following: Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and Orthonormality – Relationship Between Vectors and Signals – Signal Spaces – Concept of Convergence – Hilbert Spaces for Energy Sig... | <p>For wavelet I would recommend this book:
<a href="http://www.conceptualwavelets.com/book.html" rel="nofollow">http://www.conceptualwavelets.com/book.html</a></p>
<p>It is not too much mathematics included, yet in depth.</p>
| 1,045 |
time-frequency analysis | Meaning and unit of frequency in Laplace (Fourier) transform | https://dsp.stackexchange.com/questions/43733/meaning-and-unit-of-frequency-in-laplace-fourier-transform | <p>Imagine transfer function obtained by Laplace transform, for example:</p>
<p>$G(s) = \dfrac{1}{s+1}$</p>
<p>Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider this operation valid for this example).</p>
<p>What is the unit of the $\omega$? So far what I have seen... | <p>If you are dealing with the Laplace transform $G(s)$ of a <strong>time</strong> domain signal $g(t)$ and its evaluation on the imaginary axis to get the Fourier transform $G(j\omega)$ (assuming it exists) then the unit of your frequency $\omega$ is <strong>radians per second</strong> assuming the unit of the time wa... | 1,046 |
time-frequency analysis | Any examples of analysis in time domain to extact information | https://dsp.stackexchange.com/questions/35297/any-examples-of-analysis-in-time-domain-to-extact-information | <p>I am sending a 20Khz signal from my phone and capturing all the signals while doing exercise above it. Here I have a signal of a person doing "<a href="http://www.top10homeremedies.com/wp-content/uploads/2016/02/scissors-exercise.gif" rel="nofollow noreferrer">hand scissors exercise</a>"</p>
<p>I am doing analysis ... | 1,047 | |
time-frequency analysis | Standardizing signals from the same experiment setup with different recording tools | https://dsp.stackexchange.com/questions/82892/standardizing-signals-from-the-same-experiment-setup-with-different-recording-to | <p>I've been looking to merge two datasets I have, that capture instances of the same phenomenon using two different recording tools. Both are multichannel electrical signals, but the recording tools have very different properties.
I want to standardize those measures to make them hardware independent, but sadly I can'... | <p>I don't think there is a "one size fits all" answer for this. Here is one possible process assuming that your goal is "if I measure a system with both tools I should get the same result".</p>
<ol>
<li>Start with the requirements. What information/data exactly do you need and how good does it need... | 1,048 |
time-frequency analysis | Reconstruct signal from its Spectrogram only | https://dsp.stackexchange.com/questions/47820/reconstruct-signal-from-its-spectrogram-only | <p>The spectrogram of a signal throws away the phase information, but it is said to be possible to reconstruct the signal only from the spectrogram [1] via
$$s(t) = \frac{1}{2\pi s^*(0)}\int_{-\infty}^{\infty}\frac{M_{SP}(\theta,t)}{A_h(-\theta,t)}e^{-j\theta t/2}d\theta$$ where $M_{SP}$ is the chariteristic function o... | 1,049 | |
time-frequency analysis | What is the best Signals and systems Module Online course/resource/Youtube playlist? | https://dsp.stackexchange.com/questions/97832/what-is-the-best-signals-and-systems-module-online-course-resource-youtube-playl | <p>What is the best "Signals and systems" Module Online course/resource/Youtube playlist?</p>
<p>FYI, this request is for a Final Year undergrad following Bachelor's degree in EEE.</p>
<p>I have checked Neso academy, but its too long and can be frustating to complete it, also it doesnt cover most of the advan... | 1,050 | |
time-frequency analysis | Analysis of vibration signals | https://dsp.stackexchange.com/questions/43157/analysis-of-vibration-signals | <p>I have a vibration signal coming from a motor measured from accelerometer (<strong>Irregular Time series</strong>) and I need to use these signals for analysis purpose. </p>
<p><img src="https://i.sstatic.net/yNYDe.jpg" alt="pic2"></p>
<p>I am in need to transform this signal to some form for analysis purpose. I r... | <p>The first peak is the DC component of your spectrum which is large compared to the AC components (your signal doesn't have negative value and its always above zero which lead to large DC bias)</p>
<p>Find average of your signal over time and subtract it from your signal to remove the DC component.</p>
<p>Good luck... | 1,051 |
time-frequency analysis | How to show the time history of a signal down-sampled ? under the rate of 25Hz & 40Hz and find its DFT analysis? | https://dsp.stackexchange.com/questions/23492/how-to-show-the-time-history-of-a-signal-down-sampled-under-the-rate-of-25hz | <p>How to show the time history of a signal down-sampled under the rates of 25Hz & 40Hz and find its DFT analysis using Matlab ? The sample signal is in a data file (<a href="http://www.filedropper.com/sensordata" rel="nofollow">sensor_data.mat</a>) its sampling rate is 1000Hz.</p>
<p>I can get the time history an... | 1,052 | |
time-frequency analysis | Accelerometer data analysis without FFT | https://dsp.stackexchange.com/questions/70179/accelerometer-data-analysis-without-fft | <p>I have a device (Large as typical PC casing) with a motor. There can be a condition that the device motor load is unbalanced and the device starts to move around the table and I need to detect this. For this, I have an accelerometer.</p>
<p>But the problem is that I can't come up with a reliable algorithm to detect ... | 1,053 | |
time-frequency analysis | Why does the Hilbert-Huang transform not suffer from the uncertainty principle, and what are the implications of this? | https://dsp.stackexchange.com/questions/64336/why-does-the-hilbert-huang-transform-not-suffer-from-the-uncertainty-principle | <p>I have been studying the Hilbert-Huang transform, which I understand is a frequency analysis technique that uses the adaptive IMFs basis components to decompose a signal using EMD.</p>
<p>I understand that frequency analysis techniques such as the STFT (short-time Fourier transform) and Wavelet transform involve th... | <p>I'm not that familiar with the Hilbert-Huang transform, so I won't comment on that.</p>
<p>You seem to be under the impression that the DFT "suffers from the uncertainty principle". This is not true. Don't feel bad about thinking that as it is a widespread misunderstanding. This is a quote from an email to me fr... | 1,054 |
time-frequency analysis | Spectral entropy and moments and non stationary signal processing | https://dsp.stackexchange.com/questions/49809/spectral-entropy-and-moments-and-non-stationary-signal-processing | <p>What is Spectral entropy and spectral moments? I know what the normal entropy of a signal is! And also what are some good time-frequency features for the analysis of non-stationary signals?</p>
| 1,055 | |
time-frequency analysis | Reconstruction of batch-acquired signal | https://dsp.stackexchange.com/questions/87036/reconstruction-of-batch-acquired-signal | <p>I am currently working on a project which requires evaluating slow changes over time in the magnitude of a signal's high frequency (over 10 kHz) components.</p>
<p>This signal was acquired in tests with a 25.6 kHz sampling rate and in "batches": every minute, one second of data was acquired. This was done ... | 1,056 | |
time-frequency analysis | "Fourier Transform can localize signals in frequency domain, but not in time domain." -- What does it mean in layman's terms? | https://dsp.stackexchange.com/questions/33474/fourier-transform-can-localize-signals-in-frequency-domain-but-not-in-time-dom | <p>I was studying the introduction to wavelets and its benefit over the frequency domain. I said that:</p>
<blockquote>
<p>Fourier analysis can't localize signals both in time and frequency
domain. Fourier analysis can localize signal in frequency domain very
well, but not so much in time domain. While wavelet h... | <p>In the Fourier transform, the basis functions are complex exponentials. These functions are perfectly localized in the frequency domain, i.e., they exist at one frequency, but they have no time localization because of their infinite duration. The localization of a function depends on its spread in time and frequency... | 1,057 |
time-frequency analysis | FFT with High Time and Frequency Resolution | https://dsp.stackexchange.com/questions/82743/fft-with-high-time-and-frequency-resolution | <p>Can anyone describe in a bit more detail or provide references to the techniques for simultaneous enhancements to time and frequency resolution described in a high level in <a href="https://youtu.be/BQRNPXkN6Ww" rel="nofollow noreferrer">HEAD acoustics International - Advanced FFT Analysis HSA - frequency and time r... | <p>As Jazzmaniac said in his comments: this is a marketing video which is heavy on hype and light on technical details.</p>
<p>There is no way around the basic limitation of frequency and time resolution. The techniques used in HSA appear to be standard interpolation methods: you can adjust hop size and window length i... | 1,058 |
time-frequency analysis | When is perfect analytic filtering (discrete) suboptimal? | https://dsp.stackexchange.com/questions/84638/when-is-perfect-analytic-filtering-discrete-suboptimal | <p>Defined as "negative DFT bins zero", when are such filters suboptimal for AM/FM extraction or related filtering? <a href="https://dsp.stackexchange.com/a/83991/50076">This answer</a> reads,</p>
<blockquote>
<p>[nulling] also has the worst performance compared to other methods such as windowing or using the... | 1,059 | |
time-frequency analysis | Why we need Frequency and Time information at the same time | https://dsp.stackexchange.com/questions/14404/why-we-need-frequency-and-time-information-at-the-same-time | <p>The big disadvantage of a DFT is that it has only frequency resolution and no time resolution. This means that although we might be able to determine all the frequencies present in a signal, we do not know when they are present. So we go for Wavelets.</p>
<p>My question is, What are the applications (other than mus... | <pre><code>For the source, go to end of the answer
</code></pre>
<p>Suppose one day you got one note which has some thing written to it, say <strong>"Major frequency components are 10 Hz, 25Hz, 50 Hz and 100 Hz"</strong>. Somehow, you understood that its time-series representation is a very important thing (may be mas... | 1,060 |
time-frequency analysis | What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform? | https://dsp.stackexchange.com/questions/6266/whats-the-difference-between-the-gabor-morlet-wavelet-transform-and-the-constan | <p>At a glance, the constant-Q fourier transform and the complex <a href="https://dsp.stackexchange.com/q/2114/29">Gabor-Morlet wavelet</a> transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, etc. But maybe there's a difference that I'm missing?</p>
<p>... | <p>Simply speaking both the const-Q-transform and the Gabor-Morlet wavelet-transform are just continuous wavelet transforms. Or, more precisely, approximations thereof, as there will always be discretization issues in real applications.</p>
<p>A property of wavelet transforms is that they have build in the constant Q-... | 1,061 |
time-frequency analysis | Non-Linear, Non-Stationary spectral analysis methods! When and where? | https://dsp.stackexchange.com/questions/59797/non-linear-non-stationary-spectral-analysis-methods-when-and-where | <p>I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (HT) to get instantaneous phase and frequency.</p>
<p>However I have been doing some analysis on a non-linear, non-s... | <p>Non-linearity and non-stationarity are <strong>non-properties</strong>. Without more details, they do not say much about the methods that may perform well, and moreover the choice depends a lot on what you really do: analysis, feature extraction, enhancement, filtering, component separation, restoration? What follo... | 1,062 |
time-frequency analysis | Is it possible to extract peak locations in the time domain using help from fourier/wavelet analysis? | https://dsp.stackexchange.com/questions/59118/is-it-possible-to-extract-peak-locations-in-the-time-domain-using-help-from-four | <p>The signal I'm studying has fundamental frequencies of 20 and 60 cycles per minute (shown in the Periodogram graph). It is straight forward to extract the peaks in the time domain belonging to the 20 cycles/minute frequency (both are circled), however the peaks associated with the 60 cycles per minute frequency can ... | <p>You can figure where the peaks would be if the other tone wasn't there by an accurate estimate of the phase. This location will be a rougher estimate in the presence of the other tone. When you add a slanted signal (say a line) to a mode (a peak), it will shift the location of the peak somewhat. Since you are int... | 1,063 |
time-frequency analysis | Feature recognition within a single song | https://dsp.stackexchange.com/questions/36963/feature-recognition-within-a-single-song | <p>I want to write an algorithm in C++ which is capable of identifying specific features within a single song, e. g. the sound of a drum which is played 100 times during 5 min. </p>
<p><strong>State of the project</strong></p>
<p>So the first thing I did was to import my *.wav-file, perfrom a step-wise FFT of the sig... | 1,064 | |
time-frequency analysis | Frequency and Order maps | https://dsp.stackexchange.com/questions/64228/frequency-and-order-maps | <p>I'm new to python and I'm using it to analyse accelerations from an accelerometer ie. vibration analysis. For that I need to plot 2 types of diagrams:
1) Frequency map; frequency and time on the axis with the amplitudes,
2) Order map; order and time (or RPM) on the axis with respective amplitudes.</p>
<p>The data f... | 1,065 | |
time-frequency analysis | Plot Background Noise | https://dsp.stackexchange.com/questions/49778/plot-background-noise | <p>I am a total newbie in signal processing.
I have been trying to plot on simulink a time/frequency domain noise in PLC (Powerline Communication) that matches a real-world research <a href="https://ieeexplore.ieee.org/abstract/document/5478758/" rel="nofollow noreferrer">"<code>Time Frequency Analysis of Noise Genera... | 1,066 | |
time-frequency analysis | FFT analysis of longer data sets | https://dsp.stackexchange.com/questions/15151/fft-analysis-of-longer-data-sets | <p>I have a problem with a FFT analysis in MATLAB, which is probably related to my limited understanding of the fundamentals of Fourier analysis. </p>
<ul>
<li>I use MATLAB’s built-in fft analysis function. </li>
<li>The sampling frequency is 48000Hz The samples signal is a fairly clean sinus at 3000Hz (se below)</l... | <p>actually decreasing sampling frequency may create the aliasing effect (sampled signal will be distorted and nothing similar to the original one) </p>
<p><a href="http://en.wikipedia.org/wiki/Aliasing" rel="nofollow">http://en.wikipedia.org/wiki/Aliasing</a></p>
<p>if You want to properly sample Your signal use Nyq... | 1,067 |
time-frequency analysis | Compressing a time-domain signal in the frequency domain Matlab | https://dsp.stackexchange.com/questions/30602/compressing-a-time-domain-signal-in-the-frequency-domain-matlab | <p>I'm new to frequency domain analysis. Let's say I have a frequency domain representation from a time domain signal. What I want to do is taking frequencies with a low amplitude out of this frequency domain representation and then convert this frequency domain representation back to the time domain such that the resu... | <p>Everything depends on what you call compressing. What you are proposing is Fourier or spectrum thresholding. You will generate a $50$-length vector with some zeroes, hopefully. Let us ignore "complexness" that requires two floats for now, you can deal with it using Hermitian symmetry. </p>
<p>Your main problem is ... | 1,068 |
time-frequency analysis | Wigner-Ville Distribution (WVD) vs STFT for Spectral Analysis | https://dsp.stackexchange.com/questions/86211/wigner-ville-distribution-wvd-vs-stft-for-spectral-analysis | <p>What are the Pros and Cons of using Wigner-Ville Distribution for spectral analysis of a signal vs taking the STFT. When is it appropriate to use one over the other and is WVD used in real-time implementations?</p>
<p><strong>Update:</strong> Since no answers were received for the first few days of this post, I trie... | <p>I preface this answer with that I know little about WVD and never worked with it, but do know time-frequency, and synchrosqueezing, which shares similarities. Part of my answer will be for SSQ.</p>
<h3>Re: ChatGPT</h3>
<blockquote>
<p>The WVD is a time-frequency representation that provides a high degree of resoluti... | 1,069 |
time-frequency analysis | wavelet analysis normalized to have unit energy | https://dsp.stackexchange.com/questions/7822/wavelet-analysis-normalized-to-have-unit-energy | <p>I am analyzing some time series of sea surface water temperature and am using wavelet analysis to do so. I am computing the continuous wavelet transform and then removing some specific frequencies and then converting the series back from the frequency to the time domain. I am following the methods of torrence and co... | <p>Take the mean of the original signal and add it to the reconstructed signal. IIRC wavelets have no DC response, and so the reconstructed signal will have 0 mean.</p>
| 1,070 |
time-frequency analysis | Spectrogram of 493 signals at a time | https://dsp.stackexchange.com/questions/53014/spectrogram-of-493-signals-at-a-time | <p>I have been working with some seismic data and recently submitted a paper to a journal.</p>
<p>My seismic data has 493 traces: each trace are 8300 seconds long with sampling frequency of 2000 Hz.</p>
<p>One of the reviewers is asking me to generate a frequency spectrogram at the time= 2000s for all signals. My kno... | <blockquote>
<p>"I welcome the addition of a spectrogram showing many channels at one
particular time interval."</p>
</blockquote>
<p>If you don't want to include it, or don't have enough space, it is always worthwhile to put them in a supplementary file, attached to the journal, or separately on the Internet. I s... | 1,071 |
time-frequency analysis | Cepstrum analysis - Cut off frequencies displayed | https://dsp.stackexchange.com/questions/38837/cepstrum-analysis-cut-off-frequencies-displayed | <p>My inquiry is regarding the so called <a href="https://en.wikipedia.org/wiki/Cepstrum" rel="nofollow noreferrer">cepstrum</a> analysis.</p>
<p>By conducting some experiments, i have real time data at my disposal. The acquisition rate is 1600Hz.</p>
<p>I wanted to try cepstrum analysis just out of curiosity to see ... | <p>Presence of frequencies above cutoff in Cepstrum could be because of - </p>
<ul>
<li>Is lowpass filter used a perfect lowpass filter(does it removes all the frequencies above cutoff or just attenuates them) ?</li>
<li>If lowpass filter is not perfect, what are the relative magnitudes of high frequencies(abov... | 1,072 |
time-frequency analysis | Why is z (and not ω) the variable of interest for discrete time systems? | https://dsp.stackexchange.com/questions/75831/why-is-z-and-not-%cf%89-the-variable-of-interest-for-discrete-time-systems | <p>A continuous time domain system is well described by the Laplace transform. It allows to express any continuous signal x(t) as the integral sum of weighted complex and exponentially growing/decaying sine waves <span class="math-container">$e^{st} = e^{\sigma t} \cdot e^{j\omega t}$</span>:</p>
<p><a href="https://i.... | <p>The z-transform is the discrete version of the Laplace transform and in both cases z and s are the set of all complex numbers, and as such we map with the transform the time domain function into the domain of complex frequencies; signals that change in rotation only which is the Fourier Transform and in addition to ... | 1,073 |
time-frequency analysis | What Fourier analysis would be appropriate for analyzing servo position error as a function of frequency? | https://dsp.stackexchange.com/questions/96070/what-fourier-analysis-would-be-appropriate-for-analyzing-servo-position-error-as | <p>I'm looking for a Fourier analysis method that will help me with a servo position tracking problem. I'll give some background:</p>
<p>Imagine I have a control system that attempts to control a linear actuator to a submicron position. I have a following error signal in units of nanometers that I monitor. In an ideal ... | <p>Possibly the reason this question has lain fallow is because it contains a factual error, and cannot be answered as stated.</p>
<blockquote>
<p>"For my 1000nm peak following error in the time domain, 800nm correspond to frequency range X, 100 nm frequency range Y, and the remaining 100nm correspond to the remai... | 1,074 |
time-frequency analysis | Converging behaviour with upsampling in cross-correlation analysis | https://dsp.stackexchange.com/questions/96192/converging-behaviour-with-upsampling-in-cross-correlation-analysis | <p>I have performed a cross-correlation analysis using <em>scipy.signal.correlate</em> to determine the phaseshift (time delay) between two sine waves that I have recorded with a 180MHz digitizer.
To increase the resolution of the time delay, I performed upsampling with different factors. I found a oscillating, but con... | <p>thank you!</p>
<p>Yes, sure. I am using scipy.signal.resample for the upsampling.
Here is some of the code I used to produce this:</p>
<pre><code>def cross_corr(signal1, signal2, sampling_rate, upsampling,T_ns, method):
corr = signal.correlate(signal.resample(signal1,len(signal1)*upsampling),
... | 1,075 |
time-frequency analysis | FFT analysis for Vibration Signal | https://dsp.stackexchange.com/questions/40482/fft-analysis-for-vibration-signal | <p>I am working on balancing an air-spindle. For the unbalance analysis I use an accelerometer (NI device). I have the voltage signal from the accelerometer corresponding to the vibration of spindle at a particular frequency (rpm) saved in an excel file. To analyze the unbalance from this vibration signal I use the <co... | <p><strong>NOTE:</strong> (Updated noting the sampling rate and desired frequency) Your post describes extracting a 40 Hz signal at a 100,000 Hz sampling rate. Your filtering implementation will be significantly easier (and more effective) if you apply course low pass filtering and decimation to a lower rate before app... | 1,076 |
time-frequency analysis | EEG Power at specific time points | https://dsp.stackexchange.com/questions/25163/eeg-power-at-specific-time-points | <p>I'm in the process of building features for an EEG machine learning problem and have been doing some reading about what features may be useful. Turns out, that alpha band (8-12Hz) power can make a good distinction between my categories. The nuance is that for 1 category, alpha power rises and then falls over the tim... | <p>The Goertzel algorithm allows you to compute individual terms of the Discrete Fourier Transform, and is more efficient than the FFT. However, if you wish to later compute the spectrum of other bands besides alpha, Goertzel will turn out to be more computationally expensive than the FFT.</p>
<p>Unless you are seriou... | 1,077 |
time-frequency analysis | Why Fourier transform and Stockwell-transform retain the absolute phase information of one signal? | https://dsp.stackexchange.com/questions/29819/why-fourier-transform-and-stockwell-transform-retain-the-absolute-phase-informat | <p>Hello friends am studying the topic of signal processing and the Fourier transform and the s-transform and in most books as for example "Time-Frequency Signal Analysis and Processing. 2nd" of Boashash in section 5.11.2.3 says that these transforms retain the absolute phase information of the signal and I do not unde... | <p>It simply means that for a signal:
$$
x(t) = a(t) e^{j\phi(t)}
$$
that the phase information $\phi(t)$ is completely preserved in the transform
domain.</p>
<p>Time-frequency representations that use a <a href="https://en.wikipedia.org/wiki/Time%E2%80%93frequency_representation#Quadratic_forms" rel="nofollow">quadr... | 1,078 |
time-frequency analysis | How to understand the relationship between the filter time constant and the half-power cutoff frequency | https://dsp.stackexchange.com/questions/51042/how-to-understand-the-relationship-between-the-filter-time-constant-and-the-half | <p>I learned that the time constant can be computed as $\frac{1}{2 \pi f_0}$, where $f_0$ is the half-power cutoff frequency of a high-pass filter.</p>
<p>However, I was wondering how the time constant and the half-power cutoff frequency can be related. For example, if the half-power cutoff frequency is 2 Hz, why must... | <p>If you have a first order high-pass filter with transfer function</p>
<p>$$H(s)=\frac{s}{s+\omega_0}\tag{1}$$</p>
<p>then the squared magnitude of its frequency response is given by</p>
<p>$$|H(j\omega)|^2=\frac{\omega^2}{\omega^2+\omega_0^2}\tag{2}$$</p>
<p>Consequently, for $\omega=\omega_0$ we have</p>
<p>$$... | 1,079 |
time-frequency analysis | system response: time vs frequency. Why do I get different magnitudes? | https://dsp.stackexchange.com/questions/19779/system-response-time-vs-frequency-why-do-i-get-different-magnitudes | <p>I am simulating a linear system described by the following equation</p>
<p>$m \ddot{x} + c \dot{x} + k x = A \sin(\omega t)$</p>
<pre><code>Fs = 1000; % sampling frequency
tspan = 0:1/Fs:10;
m = 25;
c = 15;
k = 330000;
A = 100; % forcing amplitude
omega = 114.89; % forcing frequency
% State spac... | <p>What you are trying to do is to compare the amplitude of your signal with an amplitude of FFT peak, expecting it is the same. The thing is that amplitude of your signal is varying and FFT is taking the "average" over whole duration.</p>
<p>In such case you should use time-frequency representation of your signal, su... | 1,080 |
time-frequency analysis | Inconsistency Between Analysis and Simulation Results of Fourier Transform of a Sinc Function | https://dsp.stackexchange.com/questions/73838/inconsistency-between-analysis-and-simulation-results-of-fourier-transform-of-a | <p><a href="https://i.sstatic.net/OrSV8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OrSV8.png" alt="Sinc(10.t) Function and Amplitude Spectrum in the Frequency Domain" /></a>First of all, hello.</p>
<p>This question is about a problem that I’ve faced during an attempt to obtain both time and frequenc... | <p>I have recently answered a <a href="https://dsp.stackexchange.com/a/73640/55891">related question</a>.</p>
<p>What happens is that MATLAB <code>fft</code> is calculating a sum in the sampled points, the integral would be approximated with a (Riemann) sum.</p>
<p><span class="math-container">$$ \int_{0}^{T} f(x)dx \a... | 1,081 |
time-frequency analysis | FFT time domain average vs frequency bin average | https://dsp.stackexchange.com/questions/7527/fft-time-domain-average-vs-frequency-bin-average | <p>I have multiple trials of physiological data. I am doing a frequency based analysis to analyze power (amplitude) in certain frequencies of interest. Is averaging multiple trials of equal length and then taking a single FFT of the averaged signal vs computing FFT for each trial and then averaging the frequency bins t... | <p>Let me clarify.</p>
<ul>
<li>Fourier transform does <strong>not</strong> represent the histogram of the signal. Fourier transform is a linear transform that takes signal from time domain (complex function) to frequency domain (another complex function). It takes a complex function to another complex function.</li>... | 1,082 |
time-frequency analysis | Generalized translation on graph | https://dsp.stackexchange.com/questions/52000/generalized-translation-on-graph | <p>David I.Shuman in "<a href="https://arxiv.org/abs/1307.5708" rel="nofollow noreferrer">vertex-frequency analysis on graph</a>" claims that,"we generalize one of the most important signal processing tools – windowed Fourier analysis – to the graph setting and When we apply this transform to a signal with frequency co... | <p>To understand either of these, you first have to understand the basic premise behind Graph Signal Processing (GSP) which is to map a signal to a graph and then work with it on the "Graph space". This is possible due to certain similarities of classic DSP concepts and <a href="https://en.wikipedia.org/wiki/Algebraic_... | 1,083 |
time-frequency analysis | Formant analysis LPC (Matlab) | https://dsp.stackexchange.com/questions/71709/formant-analysis-lpc-matlab | <p>I wanted to do formant analysis using MATLAB and did everything according to the following tutorial:</p>
<p><a href="https://de.mathworks.com/help/signal/ug/formant-estimation-with-lpc-coefficients.html" rel="nofollow noreferrer">https://de.mathworks.com/help/signal/ug/formant-estimation-with-lpc-coefficients.html</... | <p>According to the documentation and my past experience with the ETSI GSM 06.10 "GSM Full Rate Speech Transcoding" standard, you should be careful in the requirements of each block of the system and the length of the segments after the pre-emphasis or segmentation blocks.</p>
<p>Probably you made it, but che... | 1,084 |
time-frequency analysis | The right way to approach z transform? | https://dsp.stackexchange.com/questions/26774/the-right-way-to-approach-z-transform | <p>I am a student learning dsp. I like the subject. I could understand the discrete time signals. When I move into z transform. I could not understand it. </p>
<p>Z transform is the mapping from discrete signal to zplane to make frequency analysis easy. It would be great if users give some tips that could help me to c... | <p>Discrete-time signals are generally written in the time domain as $x[n]$ where $n$ is an integer.</p>
<p>We want to be able to see how discrete-time systems can be used to modify these signals:
$$
y[n] = \sum_{m=1}^M a_k y[n-m] + \sum_{p=0}^P b_p x[n-p]
$$</p>
<p>The above equation is a linear, constant coefficien... | 1,085 |
time-frequency analysis | Find highest frequency of a very manky signal | https://dsp.stackexchange.com/questions/35028/find-highest-frequency-of-a-very-manky-signal | <p>I'm trying to compute the highest frequency (as can be sampled) in some pretty manky looking discrete time-dependent signals. My current method - a discrete fourier analysis - fails for some pretty awful looking but clearly oscillating signals (with discernable highest frequencies).</p>
<p>My current method is to c... | <p>I think most of your questions can be solved by subtracting then mean from the signal. Namely the all sinusoidal waves, with a nonzero frequency, have a mean of zero. So when the mean of a signal is not close to zero, then it will show up at 0 Hz (you can look at this as $\cos(0\,t)=1$).</p>
<p>After a closer look ... | 1,086 |
time-frequency analysis | How do I distinguish a 49.90 Hz sine wave from a 49.95 Hz one in a short audio recording? | https://dsp.stackexchange.com/questions/84852/how-do-i-distinguish-a-49-90-hz-sine-wave-from-a-49-95-hz-one-in-a-short-audio-r | <p>I've read an article about "mains hum" forensics in <a href="http://hummingbirdclock.info/about" rel="nofollow noreferrer">http://hummingbirdclock.info/about</a> and about <a href="https://en.wikipedia.org/wiki/Electrical_network_frequency_analysis" rel="nofollow noreferrer">Electrical network frequency an... | <p>A few routes that come to mind:</p>
<ol>
<li>Use phase information to refine your frequency estimates.</li>
<li>If you have good processing power, maybe a <a href="https://en.wikipedia.org/wiki/Constant-Q_transform" rel="nofollow noreferrer">constant Q transform</a> can help.</li>
<li>Track the hum frequency using a... | 1,087 |
time-frequency analysis | Time duration of a signal to determine the peak frequency | https://dsp.stackexchange.com/questions/15474/time-duration-of-a-signal-to-determine-the-peak-frequency | <p>I have two questions regarding signal processing:</p>
<p>1) In my analysis I generate a signal in the time domain with a frequency of 0.1 Hz. I apply the FFT and then determine the peak frequency of the signal, which should be 0.1 Hz. But I notice that when I simulate my signal for 200s, the peak frequency is alway... | <p>What window function are you using when you apply your FFT?</p>
<p>If the signal being analyzed is simply truncated on both ends, the window is rectangular. </p>
<p>Lets call the length of time that you generate your signal the analysis window and call the signal you create the "windowed signal". In this case I'... | 1,088 |
time-frequency analysis | Making longer a time domain signal by adding values on its frequency domain. What am I doing wrong? | https://dsp.stackexchange.com/questions/50075/making-longer-a-time-domain-signal-by-adding-values-on-its-frequency-domain-wha | <h2>Background</h2>
<p>Here's the thing: using software for Finite Element Acoustic Simulation I got the dataset of frequency response from a room; software works by solving the wave equation in the interval $`[f_i,f_f]`$ so results come directly in the frequency domain and we save them into a .csv file:
<a href="http... | 1,089 | |
time-frequency analysis | how can I analyze a basic sine wave for its frequency phase and amplitude at a particular point in time in matlab | https://dsp.stackexchange.com/questions/17142/how-can-i-analyze-a-basic-sine-wave-for-its-frequency-phase-and-amplitude-at-a-p | <p>How can I analyze a basic sine wave for its frequency phase and amplitude at a particular point in time in MATLAB? Are there any tools to do that? I am trying to do additive synthesis of inharmonic sounds in MATLAB, but having a great difficulty to extract the needed phase amplitude and frequency data of the partial... | <p>If your the unknown signal $x(n)$ is modeled as:
$$x(n)=A \sin(2 \pi f n+ \phi)+w(n)$$
and you want to estimate $A$,$f$,and $\phi$ accurately, you can use least square estimation. Unfortunately the cost function is nonlinear. You can use nonlinear least square in MATLAB to find the parameters as follows:</p>
<p>Mak... | 1,090 |
time-frequency analysis | Feature extraction of the magnitude and phase data from FRA (Frequency response analysis) of a device | https://dsp.stackexchange.com/questions/96473/feature-extraction-of-the-magnitude-and-phase-data-from-fra-frequency-response | <p>I have an FRA (frequency response analysis) of a device that have magnitude and phase as shown in the following figure. Since the response is look different at different frequencies based on the operating point of the device under test, I want to extract the features from this response to further use for machine lea... | 1,091 | |
time-frequency analysis | The effect of time increment $\Delta t$, frequency resolution $\Delta f$ and Gibbs phenomenon on the amplitude of the signal in the frequency domain? | https://dsp.stackexchange.com/questions/72554/the-effect-of-time-increment-delta-t-frequency-resolution-delta-f-and-gib | <p><strong>Experiment:</strong> Vibration analysis (i.e.: major concern is on transfer function or frequency response).</p>
<p>The input is an impulse (imagine as a knocking effect or knocking force), defined as a half sine curve. The output is the vibration speed of the specimen (measured by laser vibrometer). The vib... | 1,092 | |
time-frequency analysis | pitch vs playback rate | https://dsp.stackexchange.com/questions/7721/pitch-vs-playback-rate | <p>Let's say I have an audio sample, whose pitch is known to be C4 (don't wanna go in detail here, let's say I just sampled a tuned piano playing the C4 key).</p>
<p>The rules of the game are: I can only change the sample playback rate by any ratio. No pitchshifter module, no frequency analysis. If I set the playbackr... | <p>The ratio of sample playback rates should be equal to the ratio of pitches you want to obtain.</p>
<p>For example, if your C4 note was sampled at 48kHz, you'll need to play it back at $48000 \times \frac{277.18}{261.63} = 50.85kHz$ to make it sound like a C#4.</p>
| 1,093 |
time-frequency analysis | Help with denoising signal and periodogram analysis resources | https://dsp.stackexchange.com/questions/71917/help-with-denoising-signal-and-periodogram-analysis-resources | <p>This is a cross posting from the crossvalidated stack exchange as I thought this may be a better forum to ask.</p>
<p>I have a dataset consisting of respiratory time series signals of different lengths obtained from different groups of patients. I want to either classify or cluster the patients using these timeserie... | <blockquote>
<p>Firstly, I am confused if I am supposed to filter my signals to get rid of any frequencies above the Nyquist frequency. My sampling frequency is 32Hz and my time series is somewhat noisy and has some artifacts. I am also unsure of which filter to select for this.</p>
</blockquote>
<p>That ship has saile... | 1,094 |
time-frequency analysis | Matching two signals with small time drift | https://dsp.stackexchange.com/questions/53246/matching-two-signals-with-small-time-drift | <p>I have two time-domain signals sampled at 100 Hz that were measured using two different oscillators and therefore have a time drift between them. I have two synchronization points, one at the start and one at the end of the measurement (usually about 24h long).</p>
<p>The drift is very small, about 1 second for a 2... | 1,095 | |
time-frequency analysis | Why does alpha of 0.5 in detrended fluctuation analysis indicate randomness? | https://dsp.stackexchange.com/questions/72512/why-does-alpha-of-0-5-in-detrended-fluctuation-analysis-indicate-randomness | <p>I'm trying to get an intuitive understanding of the different coefficients in detrended fluctuation analysis (DFA).</p>
<p>It is used to detect fractal patterns in time series and it yields a coefficient, Alpha, which, as I understand is a Hurst coefficient mapped for different scales — the slope of which is the alp... | <p>The application of the DFA method starts with a conversion of a bounded time series under test into an unbounded process, the elements of the unbounded process being partial sums of the bounded time series sequence.</p>
<p>Let we have a (discrete-time) realization of WGN of length N. It is a bounded time series. The... | 1,096 |
time-frequency analysis | CWT Disapointing Frequency Separation | https://dsp.stackexchange.com/questions/58939/cwt-disapointing-frequency-separation | <p>I'm attempting to perform multi-resolution analysis via Continuous-Wavelet Transform (CWT) using Pywavelets. I've heard that CWT is supposed to be superior to STFT due to varying frequency content as a function of the time-window.</p>
<p>My test signal is two sinusoids of 1Hz and 5Hz, each lasting 10 seconds (see pi... | <p>The family of continuous wavelet transforms (CWT) is not, <em>per se</em>, superior to STFT. Due to its variations in scale, the CWT can be better, for instance, when:</p>
<ul>
<li>you address natural signals where transients are shorter than more stationary parts,</li>
<li>you do not know the appropriate scale of ... | 1,097 |
time-frequency analysis | Teager-Kaiser Operator vs. Hilbert Transform | https://dsp.stackexchange.com/questions/21662/teager-kaiser-operator-vs-hilbert-transform | <p>Since a couple of months I started working on the extraction (estimation) of signal frequency and amplitude components by means of two different time-frequency approaches, namely the Hilbert transform and the Teager-Kaiser energy operator.</p>
<p>I tested both methods on standard signals, such as chirps, sine, cosi... | <p>This paper may be of interest:</p>
<p>David Vakman, "On the Analytic Signal, the Teager-Kaiser Energy Algorithm, and Other Methods for Defining Amplitude and Frequency." IEEE Trans. Signal Processing. (1996)</p>
<p>Summarising from the paper:</p>
<p>$$\Psi(u) = a^2w^2 = [u'(t)]^2 - u(t)u''(t)$$
$$\Psi'(u') = a^2w... | 1,098 |
time-frequency analysis | Why is modern control theory in the time domain instead of the S-domain? | https://dsp.stackexchange.com/questions/75281/why-is-modern-control-theory-in-the-time-domain-instead-of-the-s-domain | <p>I am not sure if I am missing something, but from what I read I understand that modern control systems work in the time domain rather than the frequency frequency or S-domain.</p>
<p>Wikipedia article snapshot below:</p>
<p><a href="https://i.sstatic.net/mXuF3.png" rel="nofollow noreferrer"><img src="https://i.sstat... | <p>I would say that the difference is not about time domain or frequency domain, is more about using transfer function or state space equations.</p>
<p>The state equation for a system with a single input and a single output is</p>
<p><span class="math-container">$$\sum_{n=0}^{N} a_n \left(\frac{d}{d t}\right)^n y(t) = ... | 1,099 |
phase shift | Converting Time Shift to Phase Shift | https://dsp.stackexchange.com/questions/50461/converting-time-shift-to-phase-shift | <p>I have just started taking signal & systems lessons and here is my question:</p>
<p>If we say that <code>x0(t) = A.cos(w0t)</code>. (<em>a cosine signal with zero phase shift, w0 radian frequency)</em> And if we would like to time-shift this signal by for example <code>t1</code>.</p>
<p>The resulting phase shi... | <p>Indeed, you can apply the same technique:</p>
<p>As you said, given a sine signal with time shift $t_1$, which is $x(t)=\sin(w(t-t_1))$, this becomes $x(t)=\sin(w t - wt_1)=\sin(wt+\phi)$ and $\phi=-wt_1$.</p>
<p>Now, if you encounter a signal $x(t)=\sin(\frac{\pi}{4} t - \frac{\pi}{4})$ you identify $w=\frac{\pi}... | 1,100 |
phase shift | What is phase shift? | https://dsp.stackexchange.com/questions/75064/what-is-phase-shift | <p>I'm reading about when a <span class="math-container">$H(z)$</span> system is min phase or max phase, and I get when a system is a min phase or max phase depending on the location of the zeroes. But I don't get at all the phase shift part. on one point wikipedia says that these two transfer functions:</p>
<p><span c... | <p>Let the complex frequency response of a (real-valued) LTI system be</p>
<p><span class="math-container">$$H(\omega)=M(\omega)e^{j\phi(\omega)}\tag{1}$$</span></p>
<p>with magnitude <span class="math-container">$M(\omega)$</span> and phase <span class="math-container">$\phi(\omega)$</span>. If the input to such a sys... | 1,101 |
phase shift | IIR filter and phase shift | https://dsp.stackexchange.com/questions/24317/iir-filter-and-phase-shift | <p>I heard that an IIR filter has delay and phase shift effect, but not clearly what are they. For example, 1-pole Lowpass has 90 degree phase shift, 2-pole Lowpass has 180 degree? So does it mean two 2-pole Lowpass filters has 360 degree phase shift? Beside the HighPass, LowPass, AllPass filter, other IIR filter like ... | <p>I believe you have received no answers to your questions because your first three questions are so strange, so puzzling, that no one where to start to even begin to compose answers. See:</p>
<p><a href="http://www.bing.com/videos/search?q=digital%20filter%20phase%20response&qs=n&form=QBVR&pq=digital%20... | 1,102 |
phase shift | Frequency shift and phase shift (Doppler) | https://dsp.stackexchange.com/questions/13841/frequency-shift-and-phase-shift-doppler | <p>I'm trying to apply a frequency shift to a generated despreading code in order to find and track a broadcast signal CDMA. Expected doppler shift range of the signal from center frequency would be approx +/- 5KHz. Based on freq2 = c/(c-orbitspeed) * freq1.</p>
<p>I am wanting to shift the code based on equations, ass... | 1,103 | |
phase shift | Finding phase shift using complex exponential | https://dsp.stackexchange.com/questions/83101/finding-phase-shift-using-complex-exponential | <p>Suppose I have a sine wave <span class="math-container">$u(t) = \sin(2\pi f t + \phi)$</span> of known frequency but unknown phase shift and I want to find the phase shift. One way of doing this is multiply-and-adding <span class="math-container">$u(t)$</span> by a <span class="math-container">$\cos(2\pi f t)$</span... | <p>Two issues with your assumptions here. One in the way you are modeling the added phase and the other about he functioning of the <code>atan2</code> function.</p>
<p>You are modeling the phase as <code>u = sin(2*pi*f*t + phi0)</code> and then making the following comparison:</p>
<pre><code>I = u * cos(2*pi*f*t)... | 1,104 |
phase shift | A filter with low phase shift or no phase shift at all? Which one? | https://dsp.stackexchange.com/questions/66617/a-filter-with-low-phase-shift-or-no-phase-shift-at-all-which-one | <p>I'm seeking a good advice for a filter. Can you help me?</p>
<p>Right now I made my own simple filter. Not sure what I'm doing, but it seems to work.</p>
<pre><code>function testFilter (t, y, p)
% Forward filtering
% Do first filtering by jumping k/2 elements in the future
l = length(t);
ye = y;
f... | <p>If your filter is <span class="math-container">$h[n] \leftrightarrow H(e^{j\omega})$</span>, then the DTFT of the time reversed filter <span class="math-container">$h[-n]$</span> is <span class="math-container">$H^*(e^{j\omega})$</span>. Consider the result of passing your signal through the combined filter <span cl... | 1,105 |
phase shift | Phase shift between two signals | https://dsp.stackexchange.com/questions/33485/phase-shift-between-two-signals | <p>So I got some oscilloscope captures for a project I'm doing and I'd like to find a phase shift between them because I don't trust the scope calculation. </p>
<p>So I extracted data from a .csv file and loaded it into Matlab and now I'd like to find a phase shift using FFT (I think). Is there a way to do this even t... | <p>Your waveforms appear to have a low enough noise level to use interpolation of FFT results for phase estimation. First do an fftshift (to rotate the data halfway around your FFT vector) so that the FFT result phase reference point is in the center of you original data (not at the discontinuity or edges of your wave... | 1,106 |
phase shift | How to build a phase shifter with arbitrary phase shift | https://dsp.stackexchange.com/questions/31597/how-to-build-a-phase-shifter-with-arbitrary-phase-shift | <p>Fred, a DSP engineer, goes to his favorite DSP store to do some shopping.</p>
<p><strong>Fred:</strong> Hi, I'd like to buy a phase shifter.</p>
<p><strong>Shop assistant:</strong> Hmm, what exactly do you mean?</p>
<p><strong>Fred:</strong> Well, you know, if you put in a sinusoid like $x(t)=\sin(\omega_0t)$ you... | <p>Nice question! It uses one of my favorite trig identities (which can also be used to show that quadrature modulation is actually simultaneous amplitude and phase modulation).</p>
<blockquote class="spoiler">
<p> The Hilbert transform of $\sin(2\pi f_0t)$ is $-\cos(2\pi f_0t)$. Also, $$\sin(2\pi f_0t+\theta)=a\sin... | 1,107 |
phase shift | Confusion in Phase Shift Keying | https://dsp.stackexchange.com/questions/41039/confusion-in-phase-shift-keying | <p>What is the difference between Digital phase modulation(DPM) and Phase shift keying (PSK)? <a href="http://suraj.lums.edu.pk/zartash/publications/2007-DigitalPhaseMod.pdf" rel="nofollow noreferrer">http://suraj.lums.edu.pk/zartash/publications/2007-DigitalPhaseMod.pdf</a> It says that PSK is a special case of DP.</p... | <p>Phase shift keying is linear modulation.</p>
<p>Digital phase modulation is not necessarily linear.</p>
| 1,108 |
phase shift | How to achieve an arbitrary phase shift? | https://dsp.stackexchange.com/questions/59270/how-to-achieve-an-arbitrary-phase-shift | <p>To help demonstrate why a time delay appears as a linear phase shift and not a constant phase shift I wanted to plot what a constant phase shift looks like.</p>
<p>I have been looking at the Hilbert transform, which shifts the phase (of positive frequencies) by <span class="math-container">$-90^\circ$</span>, but I... | <p>You can't design a filter that creates a phase shift that's constant with frequency for real valued input (if that's what you are trying to do).</p>
<p>A Hilbert transformer appears to be doing this. However, the problem is, you can't implement a perfect Hilbert transformer since it's non causal with an infinite l... | 1,109 |
phase shift | Apply Phase Shift Using FFT and complex exponential | https://dsp.stackexchange.com/questions/95727/apply-phase-shift-using-fft-and-complex-exponential | <p>I would like to apply a phase shift by multiplying by a complex exponential in Fourier space, then taking the inverse transform. I've almost got it, but it's a factor of 2 off. I want the phase shift to be <span class="math-container">$\pi/4$</span>, but it's showing a shift of <span class="math-container">$\pi/2$</... | <p>Recall the time shift property of the Fourier Transform:
<span class="math-container">$$\mathcal{F}\{x(t - t_0)\} = e^{-j\omega t_0}X(\omega )$$</span></p>
<ol>
<li><p><code>n = np.arange(len(t))</code> is wrong. You need the indices of the frequency bins used by the FFT: <code>n = np.fft.fftfreq(len(t), 1 / Fs)</... | 1,110 |
phase shift | Digital beamforming and phase shift stage insertion | https://dsp.stackexchange.com/questions/64093/digital-beamforming-and-phase-shift-stage-insertion | <p>I have read some literatures about the different topologies of beamforming and it came to my mind a question : where is applied the phase shift for each channel depending on the type of topology/technology used?</p>
<p>For analog beamforming, it is obvious as there is only one signal, the modulated carrier signal w... | <p>In a first analysis, it does not matter where the phase shifting is inserted, as long as the mixing stage is linear.</p>
<p>Indeed, shifting a temporal signal is equivalent to multiplying it with a complex number integration the phase shift <span class="math-container">$\theta$</span> :</p>
<ul>
<li>Unshifted sign... | 1,111 |
phase shift | Phase shift of non-isosceles triangle wave | https://dsp.stackexchange.com/questions/91541/phase-shift-of-non-isosceles-triangle-wave | <p>I am researching a dynamic system. It takes in a sine wave <code>A*sin(2*pi*f*t) + D</code> and outputs a non-isosceles triangle wave. Let's call input signal SP and output signal PV. I want to create amplitude and phase characteristics of this system. I have taken measurements of SP and PV for different <code>f</co... | <blockquote>
<p>Is there a standard way of determining a phase shift between a sine wave and a non-isosceles triangle wave?</p>
</blockquote>
<p>Not really. The operation you describe is highly non-linear so the concept of a transfer function doesn't apply.</p>
<p>Probably the best you can do here is to define the phas... | 1,112 |
phase shift | phase shift between two images (matrices) | https://dsp.stackexchange.com/questions/24611/phase-shift-between-two-images-matrices | <p>I'm trying to find the phase shift between two 100x100 matrices, s and p. To start with I'm using two sine waves (2D) slightly shifted. I manage to compute the correct amplitude spectrum (using the Fourier Transform of the cross correlation between s and p) but the phase value at the peaks is not the one that I have... | 1,113 | |
phase shift | Phase shift problem in Fast Fourier Transform | https://dsp.stackexchange.com/questions/51841/phase-shift-problem-in-fast-fourier-transform | <p>I try to make graph/print for magnitudes and phase shifts for impulse response calculated by FFT.
For magnitude everything works perfect, but for phase shift I get some strange curve for higher frequencies. I can't figure out why. Could anyone help me?</p>
<p>I calculate phase shift by that:
<code>atan2(fftOutput.i... | <p>Something is wrong with your FFT. This looks like your input signal is either time reversed or shifted (circular) by one sample to the left. </p>
| 1,114 |
phase shift | Audio phase shift using Hartley Transform | https://dsp.stackexchange.com/questions/24357/audio-phase-shift-using-hartley-transform | <p>I want to shift the response phase of an audio signal (float array, length N, value range -1..1). I'm about using Fast Hartley Transform to transform it to the frequency-domain, process phase shift, then convert back to the time-domain and output the result.<br/>
I'm now can do the Hartley transform, and I also can ... | <p>I think your notation is a bit fishy but I'll use it. Assuming that your $\text{phase}(k)$ calculation is correct, do a complex multiplication of $\text{real}(k) + i\ \text{imag}(k)$ by $e^{i\alpha} = \cos(alpha) + i\sin(alpha)$. That can be done using four real multiplications and a few add/sub. Then you need to re... | 1,115 |
phase shift | Reasoning Behind Additional Phase Shift in DPSK | https://dsp.stackexchange.com/questions/30252/reasoning-behind-additional-phase-shift-in-dpsk | <p>In MATLAB's Comm System Toolbox there is an option for 'Phase Rotation', defined as the phase difference between previous and current modulated symbols when the input is zero. This is the first time I've heard of this concept. </p>
<p>Let's take DQPSK as an example. Say my previous symbol had an absolute phase of $... | <p>A QPSK constellation could in theory have any rotation. For example, $$\mathcal{S}=\lbrace 1, j, -1, -j \rbrace $$ is a QPSK constellation, and $e^{j\phi}\cdot\mathcal{S}$ is also a QPSK constellation. Matlab's <code>phaserot</code> parameter in the <code>dpskmod</code> command is $\phi$ in the equation above.</p>
... | 1,116 |
phase shift | Phase shift of discrete cosine transform (DCT) | https://dsp.stackexchange.com/questions/72892/phase-shift-of-discrete-cosine-transform-dct | <p>The most common type of discrete cosine transform (DCT-II) is defined as
<span class="math-container">\begin{align}
X_k&=\sum_{n=0}^{N-1}x_n\cdot \cos\left(\frac{\pi}{N}\left(n+\frac{1}{2}\right)\cdot k\right)&\text{where }& k=0,1,...,N-1
\end{align}</span>
(c. f. <a href="https://en.wikipedia.org/wiki/D... | <p>I think that phase shift is what causes the DCT-II to have different boundary properties compared to the DCT-I, as shown on the <a href="https://en.wikipedia.org/wiki/Discrete_cosine_transform#Informal_overview" rel="nofollow noreferrer">DCT Wikipedia page</a>. It means that it is even around <span class="math-conta... | 1,117 |
phase shift | Calculate Phase Shift Using FFT | https://dsp.stackexchange.com/questions/88501/calculate-phase-shift-using-fft | <p>I'm not a specialist in this field and learnt FFT fairly recently.</p>
<p>I want to calculate phase difference of between 1 MHz signals sampled at 4 MHz. The sample counts are both 144. I think the magnitudes and the frequencies are all correct. But phase shifts are off.</p>
<p>So, I decided to go back and start wit... | 1,118 | |
phase shift | Binary and Quadrature Phase Shift Keying | https://dsp.stackexchange.com/questions/60902/binary-and-quadrature-phase-shift-keying | <p>I was learning Modulation Techniques and was on the topic Phase Shift Keying (PSK). As far as I have understood, </p>
<p>In Binary PSK we encode a single bit on a one signal element and we differentiate between two bits (or two signal elements) by their different phase. And that it's favorable to keep the phase di... | <p>(1) The phases are indeed relative. The numbers 45, 135, 225 and 315 are relative to the transmitter's oscillator. The receiver, of course, has a different oscillator, so it will need to do some procesing to estimate the phases.</p>
<p>Related to this subject, there is also differential modulation, where 1s and 0s ... | 1,119 |
phase shift | How to calculate arbitrary phase shift in discrete signal? | https://dsp.stackexchange.com/questions/48976/how-to-calculate-arbitrary-phase-shift-in-discrete-signal | <p>When I have digital audio signal, represented in samples, I can easily phase-shift the signal by 180° by simply inverting the value of each sample.</p>
<p>But what if I want to phase shift an arbitrary voice audio signal by say +90° or -90°?</p>
<p>How do I transform an arbitrary, discrete signal by phase-shifting... | <p>The answers to <a href="https://dsp.stackexchange.com/q/31597/4298">this question</a> explain the solution for the continuous-time case. In discrete time, the solution is completely analogous. The impulse response of a phase shifter with phase shift $\theta$ is given by</p>
<p>$$h[n]=\cos(\theta)\delta[n]+\sin(\the... | 1,120 |
phase shift | Sine wave phase shift from Fourier Transform | https://dsp.stackexchange.com/questions/23655/sine-wave-phase-shift-from-fourier-transform | <p>This is probably a really basic question but I'm a little stumped and would appreciate some practical input on how to go about doing this rather than reading dockets of equations semi-related to what I am doing. </p>
<p>So say I have data which is largely reminiscent of a sine wave. I do an forward Fourier transfor... | 1,121 | |
phase shift | FIR Filter phase shift and stability | https://dsp.stackexchange.com/questions/23369/fir-filter-phase-shift-and-stability | <p>I designed an FIR highpass filter which is causing a phase shift to the output. The output signal is also not stable (?) on start.
Are these normal or am I doing something wrong?
If these are normal, what causes these?
(Attached is a diagram showing the input in blue and the output in red).<img src="https://i.sstat... | <p>This is perfectly normal. At the beginning you see the transient effect because the signal suddenly starts and the filter was at rest before (zero initial condition). A causal filter will always add some phase shift to your signal. This phase shift is usually frequency dependent, but for a <em>linear phase</em> FIR ... | 1,122 |
phase shift | Phase shift and phase spectrum terms in multidimensional signal | https://dsp.stackexchange.com/questions/22711/phase-shift-and-phase-spectrum-terms-in-multidimensional-signal | <p>I know about <a href="http://whatis.techtarget.com/definition/phase" rel="nofollow">phase of a 1D signal</a>. But when I go into higher dimensions like 2D,3D etc, it becomes headache to grasp the concept. </p>
<ul>
<li>What are the terms phase shift and phase spectrum mean in case of multidimensional(2D,3D etc.) si... | <p>For a real signal, the <strong>magnitudes</strong> of the Fourier transform bins tell what are the amplitudes of the sinusoidal components that an infinite tiling of the signal frame can be decomposed into. The <strong>phases</strong> of the bins encode <strong>translation</strong> of the sinusoids along their direc... | 1,123 |
phase shift | frequency domain phase shift | https://dsp.stackexchange.com/questions/9154/frequency-domain-phase-shift | <p>While going through FFT I came to know that, shifting of phase in frequency domain results on shifting of time in time domain.</p>
<p>According to this, in wireless communications, from the transmitter side having 2 antennas,signal s1 transmitted from Ant 1 and phase shifted version of sig2 in frequency domain tran... | <p>Suppose one signal is $a_1(t) = \cos(\omega t)$ and the other is
$a_2(t) = \cos(\omega t - \theta)$. Note the
phase shift $\theta$ between the two signals, and note also that we can write
$$a_2(t) = \cos(\omega t - \theta)
= \cos\left(\omega\left(t-\frac{\theta}{\omega}\right)\right)
= \cos(\omega (t - t_0)) = a_... | 1,124 |
phase shift | Removing Phase shift in ECG signal | https://dsp.stackexchange.com/questions/89069/removing-phase-shift-in-ecg-signal | <p>I have ECG signal sampled at 100Hz & using Python to remove noise, and generate a template signal from the collection of ECG from a total of almost 4700 signals. I have removed the noise from ECG using PCA and now looking to 'stack' together signals on top of each other to generate a template signal which will s... | 1,125 | |
phase shift | Using Goertzel to find phase shift | https://dsp.stackexchange.com/questions/23944/using-goertzel-to-find-phase-shift | <p>I have two signals with nearly the same frequency, and i would like to find the phase shift between them, since i am using micro-controller, i would like to do it in the less expensive way.</p>
<p>I know how to calculate Goertzel for a specific frequency bin (for each signal), but how do i calculate the angle for t... | <p>If the complex frequency bin outputs of the two Goertzel filters are $a$ and $b$, you can calculate the phases as $\alpha = \text{atan2}\left(\text{Im}(a),\ \text{Re}(a)\right)$ and $\beta = \text{atan2}\left(\text{Im}(b),\ \text{Re}(b)\right)$, where $\text{Re}$ returns the real component and $\text{Im}$ returns th... | 1,126 |
phase shift | Calculate phase shift between two signals | https://dsp.stackexchange.com/questions/10723/calculate-phase-shift-between-two-signals | <p>Consider the measurements of two modulated AC signals (voltage and current) which may have noise, harmonics and a DC bias. Each measured signal consists of a list for the time and a list for the corresponding values.</p>
<p>My goal is to find out the phase shift in degrees between these two signals in a robust way.... | <p>Do this procedure on both signals, and subtract the results to get what you want (it would be a nearly constant sequence whose value is phase shift in radians)</p>
<ol>
<li><p>Perform FFT on the signal to obtain its spectrum.</p></li>
<li><p>Find the dominant harmonic of the signal : $f_c$ (where the peak of FFT oc... | 1,127 |
phase shift | What's wrong with 180 degree phase shift in QPSK? | https://dsp.stackexchange.com/questions/93604/whats-wrong-with-180-degree-phase-shift-in-qpsk | <p>I red that 180 degree phase shift causes spurious high frequency components which As a result methods such as OQPSK are invented, but I can't understand how it can happens? In fact, I can't find any connection between 180 degree phase shift and the creation of high frequency components. or for example why 90 degree... | <p>OQPSK is used specifically to limit the peak-avg ratio of the QPSK waveform, as it avoids transitions from going through the origin. When the modulation in QPSK changes from one point in the constellation to another that is opposite (which is a 180 degree phase transition), the transition with go through or near the... | 1,128 |
phase shift | Phase shifting of 50Hz signal | https://dsp.stackexchange.com/questions/4709/phase-shifting-of-50hz-signal | <p>What are Method to phase shift 50 Hz digital signal using microcontroller. Appart from storage of samples to array and shift sample wise,how to shift this signal fractionally.</p>
| <p>You do it by creating a windowed sinc filter that has a wide enough pass-band to preserve the energy of whatever it is you are trying to phase shift. Instead of centering the sinc function, though, you shift it by whatever phase shift you want to introduce. You then filter the signal, which will now have that phas... | 1,129 |
phase shift | How does a shift in time domain result in phase shift in frequency spectrum? | https://dsp.stackexchange.com/questions/65891/how-does-a-shift-in-time-domain-result-in-phase-shift-in-frequency-spectrum | <p>I am aware of the fact that a time shift of say <span class="math-container">$t_0$</span>, results in a phase shift in the frequency spectrum. What confuses me is how this scales the rotational part of the transform by <span class="math-container">$t_0$</span> and doesn’t add a factor of <span class="math-container"... | <p>Consider first that in the time domain that a phase rotation or shift in phase or phase shift specifically is done by multiplying the waveform with <span class="math-container">$e^{j\phi}$</span> which rotates or shifts the complex phase for each sample in time by <span class="math-container">$\phi$</span>. Realize ... | 1,130 |
phase shift | Compensate for phase shift of Hilbert transform | https://dsp.stackexchange.com/questions/16507/compensate-for-phase-shift-of-hilbert-transform | <p>I'm using Octave and trying to use the "instfreq" function from the <a href="http://tftb.nongnu.org/" rel="nofollow">time frequency toolbox</a> which requires an analytic signal input. To get this analytic signal I'm using the Octave function "hilbert" on my real valued signal thus:</p>
<pre><code>analytic_sig = hi... | <p>1) A Hilbert transform has a very very long impulse response (above some given noise floor), so you need a ton more data to manufacture an analytic signal, otherwise you won't have enough to span the width of the Hilbert impulse response filter without serious edge truncation effects.</p>
<p>2) Instantaneous freque... | 1,131 |
phase shift | Something like Hilbert Transform to obtain arbitrary Phase Shift? | https://dsp.stackexchange.com/questions/72009/something-like-hilbert-transform-to-obtain-arbitrary-phase-shift | <p>I was wondering if there is something like a Hilbert Transform but that can implement an arbitrary phase shift to every frequency component.</p>
<p>I mean, I know that the magnitude response of a "Hilbert filter" is 1 for all frequencies and the phase response is <span class="math-container">$-\pi/2$</span... | 1,132 | |
phase shift | Best way to implement variable phase shift on FPGA? | https://dsp.stackexchange.com/questions/31226/best-way-to-implement-variable-phase-shift-on-fpga | <p>I have an incoming digitally sampled sine wave pulse, so my FPGA has the ADC level from an I and Q channel. I want to be able to shift the phase by some arbitrary amount. </p>
<ul>
<li>What's the most efficient way to do this?</li>
</ul>
<p>The most obvious way to shift phase would be just to multiply by $e^{i\phi... | <p>The allpass you're describing is a multiplication with multiple numbers. Hence, if you want to shift your phase, the only mathematically viable and easiest way is indeed a multiplication with $e^{i\phi}$.</p>
<p>I don't see why that would be overly slow – in a modern FPGA, you'd probably utilize DSP slices to do th... | 1,133 |
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