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signal denoising | Removing periodic spike noise from ECG signal | https://dsp.stackexchange.com/questions/23681/removing-periodic-spike-noise-from-ecg-signal | <p>The signal shown in the following figure is collected from a ECG sensor. The spike noise that is observed with a periodicity of 30 seconds was traced to the periodic blip of the LED as it draws current.</p>
<p><img src="https://i.sstatic.net/qsV5D.png" alt="enter image description here"> </p>
<p>The following is o... | <p>If duration of this spike is a only few point in time (1 or 2) , you can use median filter (<a href="http://en.wikipedia.org/wiki/Median_filter" rel="nofollow">wiki</a>) with size 3 or 5. But be careful - if useful signal has same duration, you will lose information.</p>
<p>P.S.<br>
As Fat32 write above, I suggest ... | 334 |
signal denoising | Denoise EEG signal by using Daubechies function | https://dsp.stackexchange.com/questions/13636/denoise-eeg-signal-by-using-daubechies-function | <p>I have an EEG signal and it contains eye blink artifacts. I read some references and know that it is possible to detect eye blinks and remove them by using wavelet transforms, but I don't know that how do it. </p>
<p>How do I detect eye blinks? After transforming the EEG signal into wavelet coefficients, what shoul... | <p>You might simply use soft/hard thresholding. This operation is quite standard and called Wavelet Denoising.
Here are some resources:</p>
<p><a href="http://www.stthomas.edu/mathematics/pdfs/MSAD/Denoising%20via%20Wavele.pdf" rel="nofollow">http://www.stthomas.edu/mathematics/pdfs/MSAD/Denoising%20via%20Wavele.pdf</... | 335 |
signal denoising | Tracking period of quasi-periodic transient type signal in strong non-stationary interference | https://dsp.stackexchange.com/questions/90256/tracking-period-of-quasi-periodic-transient-type-signal-in-strong-non-stationary | <p>Consider a desired (pink) signal as well as its observation in heavy, non-stationary interference (green, this is the desired signal plus interference). As seen in the plot, the interference can also display quasi-periodic behavior.
Initial filtering removed frequency bands where the interference dominated. The po... | 336 | |
signal denoising | Calculating Shannon-like entropy function of a 1D signal with random noise | https://dsp.stackexchange.com/questions/94589/calculating-shannon-like-entropy-function-of-a-1d-signal-with-random-noise | <p>I have been searching for a measure of Shannon's entropy <span class="math-container">$\ H $</span> or other entropy-like formulae that vary smoothly with noise for real 1D signals. MATLAB has built in functions for image entropy. The ultimate goal is to use that function for denoising with chi-square (<span class="... | <p>You're a bit missing the point here: when you use the formula <span class="math-container">$ H = - \sum_i x_i \log(x_i)$</span> instead of <span class="math-container">$ H(P) = - \sum_i p_i \log(p_i)$</span> for anything where <span class="math-container">$P(x_i) \ne x_i$</span>, then that's where your entropy estim... | 337 |
signal denoising | How to perform filtering through optimization? | https://dsp.stackexchange.com/questions/81725/how-to-perform-filtering-through-optimization | <p>I have an objective function for finding out the signal estimate say <span class="math-container">$\parallel X_{cap}-X\parallel_2^2 +$</span> denoising term. Can someone suggest me any techniques on how to incorporate a filter such as Kalman filter as an addend to this objective function in place of denoising term s... | 338 | |
signal denoising | Poisson noise and curve fitting - denoise first? | https://dsp.stackexchange.com/questions/15967/poisson-noise-and-curve-fitting-denoise-first | <p>If I have an image that is severely corrupted by Poisson noise, and I want to fit a function to the image, is it "better" to attempt to denoise the signal first before fitting, or should I move straight to the fitting stage?</p>
<p>In the example below, a 2D Gaussian function has been corrupted by Poisson noise. Sh... | <p>If the example images you've given are at all representative of your application, you may want to consider thinking about the problem a little differently. Instead of thinking of the image as "corrupted by Poisson noise", think of the observed data as a limited number of photons sampled at random from the latent ima... | 339 |
signal denoising | Why NMSE is the same as output SNR but with an opposite sign? | https://dsp.stackexchange.com/questions/81699/why-nmse-is-the-same-as-output-snr-but-with-an-opposite-sign | <p>I am doing denoising on signal, and as performance measures Normalized Mean Squared Error (NMSE) and output-SNR between original/clean and denoised signals are used.
However, for several cases the answer for NMSE and oSNR are the same but with different signs. Is it okay?</p>
<p>Input SNR for clean signal = 15 dB
O-... | <p>I mean, for fixed signal power, SNR is proportional to the inverse of noise power, and NMSE is literally the normalized inverse noise power. In decibel, inverse is just a sign change.</p>
| 340 |
signal denoising | Total Variation of a Signal - Is It Proportional to Signal Energy? | https://dsp.stackexchange.com/questions/49108/total-variation-of-a-signal-is-it-proportional-to-signal-energy | <p>In an audio application, I found it very useful to measure the <strong>total variation of a signal <span class="math-container">$y[n]$</span></strong></p>
<p><span class="math-container">$$\sum_{n=n_0}^{n_0+N} |y[n]-y[n-1]|$$</span></p>
<p>over a window of time length <span class="math-container">$N$</span> (discret... | <p>No it is not.<br />
Total Variation is like the amount of changes in the signal.<br />
Though changes require energy it doesn't mean they are proportional.</p>
<p>For instance, imagine that during a Window we see a constant signal of high value.<br />
Clearly this high energy signal (Unless energy for you is the Var... | 341 |
signal denoising | extract trend correctly, including most recent values | https://dsp.stackexchange.com/questions/50114/extract-trend-correctly-including-most-recent-values | <p>I'm looking to extract the trend of a signal.</p>
<p>i've tried two methods for now, polynomial regression, and wavelet denoising</p>
<p>both methods don't respect the computation of the last values (meaning the last values computed will not be the same if we compute a longer buffer containing new values).</p>
<p... | 342 | |
signal denoising | How to preprocess such signals? | https://dsp.stackexchange.com/questions/34334/how-to-preprocess-such-signals | <p>I am interested in denoising accerelation measurements, recorded in ambient vibration tests. Such tests consist in recording the vibrations of a mechanical structure, say a table for example. So say I put an accelerometer on the table and measure the signal without touching the table. The objective is to retrieve th... | 343 | |
signal denoising | Convex Optimization in Signal and Image Processing | https://dsp.stackexchange.com/questions/24890/convex-optimization-in-signal-and-image-processing | <p>In signal processing, convex optimization plays a useful role in problems such as sparse signal recovery and filter design. What other places does convex optimization appear?</p>
<p>For example, in compressed sensing the Basis pursuit Denoising problem, the LASSO problem and the Dantzig selector can be posed as:</p... | <p>There's a whole area of signal processing dedicated to optimal filtering. In pretty much every case I've seen the filtering problem is formulated with a convex cost function. </p>
<p>Here's a freely available book on the subject - <a href="http://www.ece.rutgers.edu/~orfanidi/osp2e/osp2e.pdf" rel="nofollow noreferr... | 344 |
signal denoising | How detect and filter noise from signal | https://dsp.stackexchange.com/questions/13119/how-detect-and-filter-noise-from-signal | <p>This is the spectrum of the signal:<img src="https://i.sstatic.net/KyDB1.png" alt="Welch method of SPD"></p>
<p>And this is the signal:</p>
<p><img src="https://i.sstatic.net/w17nt.png" alt="Original sig"></p>
<p>On the FFT spectrum you can notice the high amplitude peaks and I think these frequencies are the mai... | <p>Just "eyeballing" your signal, it looks like the interesting things are all down below 1Hz. The peaks in your signal browser diagramm seem to be spaced at every 5 to 10 Seconds, which would be 0.1 to 0.2 Hz. Your spectrum plot goes from zero to 25 Hz, and doesn't show anything really interesting.</p>
<p>Try zoomi... | 345 |
signal denoising | Avoiding latency distortion at high denoise levels with DWT | https://dsp.stackexchange.com/questions/89516/avoiding-latency-distortion-at-high-denoise-levels-with-dwt | <p>I am denoising biological signals using the DWT, and for UI reasons would prefer the smoother waveform afforded by denoise level 5. However, higher denoise levels seem to distort the latency of salient features (peaks). I've played around with different parametrizations (which converge to a function call of MATLAB'... | 346 | |
signal denoising | What are the pros and cons of wavelet for filtering compared to conventional filters? | https://dsp.stackexchange.com/questions/43951/what-are-the-pros-and-cons-of-wavelet-for-filtering-compared-to-conventional-fil | <p>Wavelets have been widely used in denoising or extracting one specific frequency band of a signal nowadays. However, these can also be done through conventional filters (e.g. butterworth, Chebyshev). So what are the pros and cons for these two methods for filtering? </p>
| <p>Let us first consider the orthogonal DWT: this transform is build with several constraints: orthogonality (and invertibility) of course, and the discretization of some continuous wavelet transform, with a specific dyadic structure, yielding a frequency decomposition whose cut are approximately:</p>
<p>$$[0\;1/2^L\;... | 347 |
signal denoising | Kalman filtering in practice: biomedical processing | https://dsp.stackexchange.com/questions/96519/kalman-filtering-in-practice-biomedical-processing | <p>I'm working with a Lead II ECG signal sampled at 500 Hz that contains noise and artifacts.
I do not have access to an accelerometer or reference signals — only the ECG itself.</p>
<p>I'm new to Kalman filters and I am trying to denoise ECG signals. I have read that Kalman Filters can be useful for this, but I am con... | 348 | |
signal denoising | Filtering artefacts and filtering short signals | https://dsp.stackexchange.com/questions/69532/filtering-artefacts-and-filtering-short-signals | <p>I have a signal from EEG sensors and I try to denoise it from AC frequencies. For that reason, I estimated PSD of my signal and found that 50 Hz and 100 Hz are likely to represent noise. I constructed Butterworth filter of order four and got much clearer signal, but at the start ([0:150] segment) there is even more ... | <p>All real-time filtering (as opposed to post processing) wirh FIR and IIR filters will have start up transitions based on the state of the filter at start up. For optimum rejection of AC noise , Instead of a Butterworth Filter consider using an 2nd order IIR notch filter with the notch set at your AC frequency (such ... | 349 |
signal denoising | Why should wavelet re-synthesis produce an output when the main component is suppressed and what does this mean for denoising? | https://dsp.stackexchange.com/questions/69441/why-should-wavelet-re-synthesis-produce-an-output-when-the-main-component-is-sup | <p>I understand that aliasing occurs in DWPT if the wavelet used is of low order since the "filters" are not perfect and the combination of down sampling and overlapping between bands causes aliasing.
I am using low order wavelet as I aim to implement the process in real-time and I have limitations on the num... | 350 | |
signal denoising | Removing low frequency vibrations from measured signal | https://dsp.stackexchange.com/questions/30690/removing-low-frequency-vibrations-from-measured-signal | <p>Suppose I have two sensors $s_1$ and $s_2$. $s_1$ measures the desired heart signal (with most of the frequency content below 100 Hz), and the other is a reference sensor picking mainly background noise. </p>
<p>Due to the pumping of the blood in the heart, there is also low frequency vibrations, mainly below 10 Hz... | 351 | |
signal denoising | How can I use interpolation to align audio | https://dsp.stackexchange.com/questions/89231/how-can-i-use-interpolation-to-align-audio | <p>I notice that when I connect two audio clips, there is a jump at the junction.</p>
<p><a href="https://i.sstatic.net/k6uLU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/k6uLU.png" alt="enter image description here" /></a>
How do I use interpolation to connect these two pieces of audio?</p>
<p>Thanks... | <p>A straightforward(ish) approach is cross-fading: apply a fade-out at the end of the first clip and a fade-in at the beginning of the second. Overlap the two sections that fade in/out, which will gradually blend the two together.</p>
<p>You can experiment with linear/logarithmic fade curves, and of course with the fa... | 352 |
signal denoising | Recommended resources for noise reduction | https://dsp.stackexchange.com/questions/51927/recommended-resources-for-noise-reduction | <p>I know the question <a href="https://dsp.stackexchange.com/q/427/36868">What Resources Are Recommended for an Introduction to Signal Processing (DSP)?</a> and I have already read some general DSP books, such as Rick Lyons's "Understanding DSP," and also have browsed through Oppenheim's.</p>
<p>More specifically, <... | <p>Signal denosing is a well-studied technique in signal processing. It first began using simple techniques such as filtering. In this approach, the emphasis is laid on designing filters which can perform denosing techniques in a fast and efficient manner.</p>
<p>Later, when wavelet theory was developed, some research... | 353 |
signal denoising | Expanding piecewise polynomial using Daubechies wavelet | https://dsp.stackexchange.com/questions/29706/expanding-piecewise-polynomial-using-daubechies-wavelet | <p>What is the best Daubechies wavelet (i.e. the number of vanishing moment) to expand a signal $\boldsymbol{x} \in \mathbb{R}^n$?
$\boldsymbol{x}$ consists of $m$ pieces of polynomial with $d$ degree. The criterium is to make the DWT signal as sparse as possible.</p>
<p>Update:
The goal of sparsifying the signal in ... | <p>According to your formula, you also apply soft-thresholding to the approximation coefficients, which is not standard. Aside, your operator $W$ does not seem to specify the number of wavelet levels used. Finally, your class of signals does not seem to address the regularity at piecewise junctions. </p>
<p>I believe ... | 354 |
signal denoising | How to acquire physical noise samples | https://dsp.stackexchange.com/questions/32278/how-to-acquire-physical-noise-samples | <p>I need to obtain some real (simulated) data to indicate noise in communication system.</p>
<p>How do I go about it? I need it for my thesis.</p>
<p>I don't know if denoising a set of signals will help so I can have the noise data samples.</p>
<p>I just need the noise data samples.</p>
| <p>One easy way to grab a set of samples of physical noise is by acquring a cheap SDR, such as an <a href="http://www.rtl-sdr.com/" rel="nofollow">RTL</a>, tuning it to an empty band, and just reading and saving the samples. This should give a you a nice set of mostly white noise samples.</p>
| 355 |
signal denoising | Detecting and Removing Noise from Signal using Python | https://dsp.stackexchange.com/questions/85013/detecting-and-removing-noise-from-signal-using-python | <p>Through this platform, I want to ask that how can I remove unwanted noise from the signal when you do not have much information regarding the frequency at which they appear? Data is collected from an inductive sensor and sampling frequency is 30000 Hz. There are a lot of electrical noises in the signal, the easily d... | <p>The train moves at speed <span class="math-container">$v_t$</span>. This (absolute) speed reasonably will have a supremum <span class="math-container">$v_{t\max}$</span>. It obviously has an infimum of <span class="math-container">$0$</span>, but there is nothing to measure with a train standing around. So we declar... | 356 |
signal denoising | Is this better detection than Matched Filter and Gaussian noise cancellation technique for SONAR data? | https://dsp.stackexchange.com/questions/93291/is-this-better-detection-than-matched-filter-and-gaussian-noise-cancellation-tec | <p>The code below generates one sinusoid and considered as known signal. One needs to find the location of the signals under additive Gaussian noise.</p>
<p>The known signals is comprise of the sinusoids with random phase and amplitude and at random location in time samples.</p>
<p>As I understand Matched filter is the... | 357 | |
signal denoising | How well can discrete wavelet packet transform reduce noises that are similar to the input signal in the same frequency band? | https://dsp.stackexchange.com/questions/69345/how-well-can-discrete-wavelet-packet-transform-reduce-noises-that-are-similar-to | <p>If I had 50Hz noise coming from power line, and signals in the same frequency range (EEG for example 0.1Hz to 100Hz). If my sampling frequency is 30kHz but I downsample my signal to 937kHz and use the discrete wavelet packet transform (with Daubechies wavelet) for denoising purposes.</p>
<p>My frequency content now ... | 358 | |
signal denoising | Detect the beginning of an increasing signal | https://dsp.stackexchange.com/questions/48996/detect-the-beginning-of-an-increasing-signal | <p>After denoising and cleaning, I get amplitude signals like this (y-axis: dB):</p>
<p><img src="https://i.sstatic.net/Pl6ob.png" width="300">
<img src="https://i.sstatic.net/UlIpe.png" width="300">
<img src="https://i.sstatic.net/6BLFB.png" width="300"></p>
<p>On bottom left of each of these 3 graphs, you can see a... | <p>It is not entirely clear what sort of signal we are dealing with here, apart from the use of the "audio" tag. If the signal had a wider bandwidth then this would be closer to <a href="https://www.google.co.uk/search?q=onset+detection" rel="nofollow noreferrer">onset detection</a>. But this is not what we are dealing... | 359 |
signal denoising | Filtering a square signal with a median filtering to preserve the edges | https://dsp.stackexchange.com/questions/69867/filtering-a-square-signal-with-a-median-filtering-to-preserve-the-edges | <p>If needed, you can find my first post for this problem <a href="https://dsp.stackexchange.com/questions/69850/applying-a-lowpass-filter-to-a-noisy-square-signal-leads-to-a-shift-of-the-signa/69851?noredirect=1#comment144072_69851">here</a>.
I am trying to clean the following signal:</p>
<p><a href="https://i.sstatic... | 360 | |
signal denoising | Classification of very noisy EMG signals | https://dsp.stackexchange.com/questions/76389/classification-of-very-noisy-emg-signals | <p>I'm an absolutely newbie to signal processing. I'm trying to classify EMG signals which are very noisy (decibel values are more than -70 dB in some cases). After applying EMD technique these values are improved to -30 dB to -40 dB.</p>
<p>My question is :</p>
<p>I want to classify these EMG signals. It's a binary c... | <p>-30 dB is still very noisy.</p>
<p>If you've had success with EMD, I'd try an inspired transform that's improved on it: <a href="https://github.com/OverLordGoldDragon/ssqueezepy" rel="nofollow noreferrer">synchrosqueezing</a>. Whether it's best to denoise before classifying depends on amount of available data: most ... | 361 |
signal denoising | How does signal subtraction affect frequency response? | https://dsp.stackexchange.com/questions/83067/how-does-signal-subtraction-affect-frequency-response | <p>I had a noisy signal which I denoised using machine learning. Now assuming the noise was additive I am subtracting the denoised signal from the noisy signal to get the noise part. I just did time domain subtraction, but when I plotted the frequency response of the noisy signal, the denoised signal and the noise, I n... | <p>Well, two options:</p>
<ol>
<li>Your channel doesn't only <em>add</em> noise, but has some nonlinearity, or the noise is not just additive, so: your model is wrong, or</li>
<li>your denoiser is not perfect and doesn't only remove noise, but maybe adds some interference at some frequencies. So: your denoiser can't de... | 362 |
signal denoising | Interpretation of Histogram in Statistical Image Processing | https://dsp.stackexchange.com/questions/35015/interpretation-of-histogram-in-statistical-image-processing | <p>I am learning statistical image processing by myself. In papers and books, it always show the histogram of original images and gradients as the following image shows. The histograms of images vary significantly while histograms of image gradients show some similarity. Does it assume that each pixel in images obey th... | <blockquote>
<p>Does it assume that each pixel in images obey the same probability distribution for the histograms of images? </p>
</blockquote>
<p>Images of different scenes will definitely not obey the same probability distribution of the pixel values. </p>
<p>Histograms are one way that people use to do dimensio... | 363 |
signal denoising | removing noise using Scipy.signal.butter: | https://dsp.stackexchange.com/questions/64008/removing-noise-using-scipy-signal-butter | <p>I am going to remove the noise from a brain recorded signal. It was a continuous recording and with sample rate=30kHz, it was digitized. So now it is a digital signal.
I have written the code here for denoising this signal and I put two figures (the red one is the denoised one) including one big picture figure and ... | 364 | |
signal denoising | denosing given signal using wavelet | https://dsp.stackexchange.com/questions/15525/denosing-given-signal-using-wavelet | <p>let us suppose that we have given following model</p>
<p>$y(t)=A_1 \sin(\omega_1*t+\phi_1) + A_2 \sin(\omega_2*t+\phi_2) + A_3 \sin(\omega_3*t+\phi_3)+ \ldots +A_p \sin(\omega_p*t+\phi_p)+z(t)$</p>
<p>where $z(t)$ is white noise,we have everything unknown,$p,A_i,\omega_i,\phi_i$,what i want to remove noise using ... | <p>If you have reason to believe your signal is sparse in the frequency domain, they you should be denoising in that: use FFTs, not wavelets. Look at the magnitude spectrum and see if it's very spiky, and that will be your cue. If so, attenuate the frequencies with a small response.</p>
| 365 |
signal denoising | What is the name of this very simple spectral subtraction technique? | https://dsp.stackexchange.com/questions/51724/what-is-the-name-of-this-very-simple-spectral-subtraction-technique | <p>Let $S = X + N$ be the sum of two audio signals $X$ and $N$ which are both stationnary (let's think X is a constant volume 440 Hz sinusoid and N is constant volume noise).</p>
<p>If the sum S has a -20 dB volume and N has a volume of -30 dB, <strong>what is the volume of X?</strong> (could be RMS or peak volume, ... | <p>Estimating the power of a sum of signals depends on coherence or incoherence assumptions. Details are given for instance on <a href="http://www.sengpielaudio.com/calculator-leveladding.htm" rel="nofollow noreferrer">incoherent signal summing</a> or <a href="http://www.sengpielaudio.com/calculator-leveladding.htm" re... | 366 |
signal denoising | Spectral analysis of positive signals | https://dsp.stackexchange.com/questions/9220/spectral-analysis-of-positive-signals | <p>Suppose that I have a sensor that can acquire samples $X[k]$ of the Fourier transform of an unknown signal $Y[t]$. An example is MRI, where the acquired data is in $k-$space. Now suppose that the unknown signal $Y[t]$ is known to be real and non-negative. My question is: is there a principled way to incorporate this... | <p>To give a complete answer to this question you're going to need to provide more details about the kind of models you're considering in the first place. But yes, in many cases you can augment those models with <em>a priori</em> constraints on $Y[t]$, such as $0 \leq Y[t] \leq 1$. </p>
<p>For example, if the standard... | 367 |
signal denoising | multi-frame image restoration | https://dsp.stackexchange.com/questions/70972/multi-frame-image-restoration | <p>Suppose we have a sequence of still images each of which has been contaminated by some particles(ex, dust/sand/smoke) making the images very poor in certain areas.</p>
<p>What approach would be best to teach image regeneration using multiple frames? The simplest technique is to simply find a way to detect what parts... | 368 | |
signal denoising | Additive White Gaussian Noise (AWGN) and Undecimated DWT | https://dsp.stackexchange.com/questions/37932/additive-white-gaussian-noise-awgn-and-undecimated-dwt | <p>One of the benefits of DWT is that it is an orthonormal transform. </p>
<p>There are statements that the energy of noise component mainly concentrates on the high-frequency (detail) part and distributes homogeneously. The energy of noise component is included in more wavelet coefficients with smaller amplitudes, wh... | <blockquote>
<p>One of the benefits of DWT is that it is an orthonormal transform</p>
</blockquote>
<p>Well, not quite. Some standard DWT are orthonormal, but not all of them. The others used in practice are biorthogonal. Which makes computations more difficult. However, for close-enough-to-orthogonal wavelet transf... | 369 |
signal denoising | If I know the RMS noise/the variance of a DC measurement, can I simply subtract it from the measurement? | https://dsp.stackexchange.com/questions/84149/if-i-know-the-rms-noise-the-variance-of-a-dc-measurement-can-i-simply-subtract | <p>Let's say I have an electronic system that's taking a measurement. It provides a simple bipolar excitation current to a resistive load (bipolar square wave so as to cancel out thermal emf), puts it through an analog front end and some anti-aliasing, into an ADC.</p>
<p>What I'm thinking is if during calibration we c... | <p>Yes. Your intuition is correct, you need some sort of a statistical method since you don't have a way to measure the noise separately from your noisy measurement synchronously (in which case what you propose would work for an offline process).<br />
What you do have is a measurement of the noise taken as a separate ... | 370 |
signal denoising | Sampling frequency after aggregations | https://dsp.stackexchange.com/questions/76845/sampling-frequency-after-aggregations | <p>I have accelerometer signal, which is preprocessed by the actigraph on-device. Original sampling rate is 32 Hz, but activity count is summed for every minute, so I have a signal with 1 measurement per minute.</p>
<p>For denoising and to analyze long-term dependencies (my data spans several days), especially related ... | <p>It depends on <em>which</em> signal you want to do frequency analysis with. If you are doing frequency analysis on the 1/3600 Hz signal, then that is the sample rate the function probably expects. If you are doing frequency analysis on the 1 Hz signal, then use 1 Hz as the sample rate parameter in the function you a... | 371 |
signal denoising | Algorithms for removing oscillations? | https://dsp.stackexchange.com/questions/15171/algorithms-for-removing-oscillations | <p>I am interested in removing oscillations from a signal to capture the lower-frequency variations, similar to the objective of <a href="https://dsp.stackexchange.com/questions/9671/how-to-remove-the-periodic-oscillations-from-a-signal">this problem</a>. The oscillations vary in frequency in the time domain, so wavele... | 372 | |
signal denoising | Filter away sinusoidal noise properly | https://dsp.stackexchange.com/questions/46033/filter-away-sinusoidal-noise-properly | <p>I have a stereo music signal corrupted by strong sinusoidal noise that varies over time. Here is the spectrogram of Left channel I plotted with Matlab.
As you can see there are 3 or 4 strong harmonics with frequency that varies over time.</p>
<p><a href="https://i.sstatic.net/noNzA.png" rel="nofollow noreferrer"><... | <p>Definitely, try to reconstruct the sine and then subtract it. A notch filter will create artifacts as the desired signal changes, with notes stopping and starting, and percussion. Even if those notes are at pitches of frequencies outside the range of the notch filter.</p>
<p>To extract the unwanted sine, use a ban... | 373 |
signal denoising | Size filtering on binary images | https://dsp.stackexchange.com/questions/59583/size-filtering-on-binary-images | <p>I have noisy images from which I extract the contours using OpencCV's <code>findCountours</code>, which performs binarization internally. This results in innumerable small outlines made of three or four pixels, which I would like to avoid.</p>
<p>I want to discard these, either before extracting the contours, or du... | 374 | |
signal denoising | Using Signal to Noise Ratio (SNR) formula for machine learning metric evaluation | https://dsp.stackexchange.com/questions/94229/using-signal-to-noise-ratio-snr-formula-for-machine-learning-metric-evaluation | <p>As the SNR function is not commutative (meaning different argument positions will lead to different output results), it makes me confused to use it as metric evaluation.</p>
<p>I have this 3 signal; those are X_test, y_test, and y_pred. Those are common naming conventions for supervised learning models. So what are ... | <p>The remaining is simply the difference between the noise signal and the clean signal. You can define 3 different SNRs here</p>
<p>The SNR of your original signal is</p>
<p><span class="math-container">$$SNR_{original} = 10\log_{10}\frac{\sum y_{test}^2}{\sum (x-y_{test})^2}$$</span></p>
<p>After the denoising the SN... | 375 |
signal denoising | Wavelet transform, scalogram, detail and approximation coefficients | https://dsp.stackexchange.com/questions/93387/wavelet-transform-scalogram-detail-and-approximation-coefficients | <p>I understand tha the wavelet transform is about computing the coefficients to assign to scaled and translated versions of the chosen mother wavelet. The coefficients measure the correlation between the signal and shifted/scaled wavelet. That said, I know that the CWT is used to compute the scalogram while the DWT is... | 376 | |
signal denoising | 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>
| 377 |
signal denoising | Detecting and removing interferences from a signal | https://dsp.stackexchange.com/questions/74625/detecting-and-removing-interferences-from-a-signal | <p>I am using MATLAB in order to denoise and remove interferences on a signal.</p>
<p>I used <code>wdenoise</code> to denoise my signal which works by setting a threshold (for example SURE) for each scale and set all coefficients below this threshold to zero (these coefficients represents noise). It works pretty well.<... | <p>I'd recommend using a <a href="https://en.wikipedia.org/wiki/Median_filter" rel="nofollow noreferrer">median filter</a> to smooth your signal. A median filter will get rid of the outliers, or the spikes in your signal. The length of the median filter will have to be determined by how frequently the spikes appear in ... | 378 |
signal denoising | Implementation of Cepstrum in Python | https://dsp.stackexchange.com/questions/69576/implementation-of-cepstrum-in-python | <p>Actually I want to denoise a signal. I know how can I implement FFT in python to denoise it. This is the implementation which I use(From <a href="https://www.kaggle.com/theoviel/fast-fourier-transform-denoising" rel="nofollow noreferrer">this</a> Kaggle notebook):
<a href="https://i.sstatic.net/qhN9h.png" rel="nofol... | 379 | |
signal denoising | Correlated signals separation with reference | https://dsp.stackexchange.com/questions/47667/correlated-signals-separation-with-reference | <p>I have a signal S, which needs to be split into two components Sx and Sy.</p>
<p>And I have a signal X, which is a reference signal corresponding to Sx. </p>
<p>I need to perform this split of S and check that resulting Sy is ~Y and Sx ~X (I can use X in the process of filtering\separation, but not Y). </p>
<p>Th... | <p>I followed the link from you more current version. I think your problem is better stated here.</p>
<p>1) I don't think you can solve it as stated. You will have a one unknown parameter family of solutions.</p>
<p>2) If you can use a portion of Y, and the coefficients remain the same, you can easily solve it.</p>... | 380 |
signal denoising | Noisy signal filtering MATLAB | https://dsp.stackexchange.com/questions/30444/noisy-signal-filtering-matlab | <p>I'm currently working on rectifying a respiratory noisy signal shown below:</p>
<p><a href="https://i.sstatic.net/l90XF.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/l90XF.jpg" alt="enter image description here"></a></p>
<p>I've already tried to filter the noise as you can see in the image below (... | 381 | |
signal denoising | FFT/PSD/IFFT analysis on single axis piezoelectric accelerometer signals for curb impacts | https://dsp.stackexchange.com/questions/74449/fft-psd-ifft-analysis-on-single-axis-piezoelectric-accelerometer-signals-for-cur | <p>I'm trying to denoise the signal by performing PSD analysis and followed by IFFT. Ultimately, I want to generate Force and Displacement plots from the denoised acceleration signal.</p>
<p>Noisy Acceleration Signal(<span class="math-container">$a_z$</span> vs t):</p>
<p><a href="https://i.sstatic.net/nNBVe.png" rel="... | <p>Filtering by zeroing out bins is not a recommended approach as it will introduce significantly more time domain ringing, as detailed here</p>
<p><a href="https://dsp.stackexchange.com/questions/6220/why-is-it-a-bad-idea-to-filter-by-zeroing-out-fft-bins">Why is it a bad idea to filter by zeroing out FFT bins?</a></p... | 382 |
signal denoising | Smoothing for damped wave signal (fixed variance noise, but changing SNR) | https://dsp.stackexchange.com/questions/34143/smoothing-for-damped-wave-signal-fixed-variance-noise-but-changing-snr | <p>My colleagues and I are arguing about how to smooth a damped wave signal.</p>
<p>This signal is corrupted by white noise of a steady magnitude.</p>
<p>However the signal damps out as it goes along. So, the SNR and the noise as a standard dev of the signal range, both decrease.</p>
<p>My colleagues say I can denoi... | 383 | |
signal denoising | Intro Question to Signal Processing (Low-Pass Filter) | https://dsp.stackexchange.com/questions/14897/intro-question-to-signal-processing-low-pass-filter | <p>I have a noisy signal file in Matlab and I have to denoise the polluted signal using a discrete Fourier transform.</p>
<p>I'm asked to perform the fourier transform, then take its absolute value. Then study/examine the absolute values to then implement a low-pass filter for the actual sound (and corresponding high-... | <p>Based on your description it sounds like the idea is to use the FFT to figure out where your signal energy is in terms of frequencies. Once you know that you know what the passband of your filter should be, and from that you can decide on a reasonable cutoff frequency. You want to cutoff as much of the noise energ... | 384 |
signal denoising | Understanding noise removal method using wavelets | https://dsp.stackexchange.com/questions/71212/understanding-noise-removal-method-using-wavelets | <p>I am trying to understand how wavelet transform can be used to denoise a time series or signal and how to plot the scalogram image. My signal has a lot of fluctuations and as such I am finding it difficult to denoise. Morevoer, to plot the scalogram I need to know the frequency. I don't know what is the frequency fo... | <p>Your signal (with initial par x0 =0.1) is already noise like and high frequency. It will be hard to distinguish it from the added white noise... One thing you can do is to interpolate (resample) the time series by a large enough factor and then later add the white noise. This will artifically help to separate the no... | 385 |
signal denoising | Unable to remove audio noise using weak signal power calculated from FFT as threshold | https://dsp.stackexchange.com/questions/94622/unable-to-remove-audio-noise-using-weak-signal-power-calculated-from-fft-as-thre | <h1>Question</h1>
<p>Please help understand the cause and solution of the problem of unable to remove the audio noise by using the signal power as filter threshold. If the approach is not correct, please advise the better or correct ways.</p>
<h1>Background</h1>
<p>Try to remove the audio noises in the <a href="https:/... | <p>I still do not completely understand the exact mechanism, but using a threshold and zero-out in the frequency domain was a wrong way as explained in <a href="https://dsp.stackexchange.com/a/6224/73490">Why is it a bad idea to filter by zeroing out FFT bins?</a>, which further broken down into the explanation in <a h... | 386 |
signal denoising | wavelet reconstruction | https://dsp.stackexchange.com/questions/48191/wavelet-reconstruction | <p>I am doing mtech project now.
Actually I am working on discrete wavelet transform.I have done till wavelet decomposition. I have been stuck in reconstructing the signal back to original .please help me out.</p>
<p>code--</p>
<pre><code>f=10;
fs=200;
amp_x = 14;
% amplitude for sinusodial 2
amp_y = 9;
% Time vector... | 387 | |
signal denoising | Adding multiple noise sources with target SNR with ECG data using the MIT BIH Noise Stress Test Database | https://dsp.stackexchange.com/questions/85700/adding-multiple-noise-sources-with-target-snr-with-ecg-data-using-the-mit-bih-no | <p>I'm new to signal processing, and I believe to understand what additive noise is. However, while reading several ECG denoising papers, I've noticed that some combine multiple noise sources from the <a href="https://physionet.org/content/nstdb/1.0.0/" rel="nofollow noreferrer">MIT BIH Noise Stress Test database</a>. ... | 388 | |
signal denoising | What do I measure in a Sound Sample Buffer to remove noise from an audio file using the Kalman Filter? | https://dsp.stackexchange.com/questions/81547/what-do-i-measure-in-a-sound-sample-buffer-to-remove-noise-from-an-audio-file-us | <p>I am developing a computer program that removes or reduces the background noise from an audio file using the Simple Kalman Filter. I have implemented the Kalman Filter and a way of obtaining the "sample buffer" for the audio file.</p>
<p>I understand how the Kalman Filter works in terms of the purpose of e... | <p>Using the <a href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.417.7052&rep=rep1&type=pdf" rel="nofollow noreferrer">AMS-based modulation-domain Kalman Filtering framework</a>, this can be done.</p>
| 389 |
signal denoising | custom raw compression | https://dsp.stackexchange.com/questions/81432/custom-raw-compression | <p>I'm planning to acquire between 50k and 200k image per day with a 50MPixels (or 68MPixels or 130MPixels) sensor; I'll be acquiring the raw data (10 or 12 or 14 bits) from the sensor through SLVS-EC and create a raw file of my own design. The raw bitrate from the sensor may go up to 75.2 Gbps.</p>
<p>I may have to st... | <p>Raw files are (ideally) the raw readout of a sensor. Suitable for research, or if you want to eek out all possible information from a sensor using fancy offline processing. Now or in 10 years. In some cases, you might not need all of the information contained in a full raw image, but be satisfied with having maksimu... | 390 |
signal denoising | What is the best to add accelerometer noise to PPG signals? | https://dsp.stackexchange.com/questions/93172/what-is-the-best-to-add-accelerometer-noise-to-ppg-signals | <p>I have a BIDMC PPG signals. I'm trying to add accelerometer data as a noise to PPG signals and trying to denoise it using deep generative models like GANs, VAEs, Diffusion Models. So, what can be the best way to add noise so that the it wouldn't distort the signal so much that we lose all the original information?</... | <p>I assume that your question refer to the stochastic noise sources of the sensor, and not to the deterministic ones (mis-alignement, scale-factors, non-orthogonalities, etc.)</p>
<p>Accelerometers tend to have three different stochastic noise sources:</p>
<ul>
<li>White Noise</li>
<li>Flicker noise (bias instability)... | 391 |
signal denoising | How does noise reduction for speech recognition differ from noise reduction that is supposed to make speech more "intelligible" for humans? | https://dsp.stackexchange.com/questions/42422/how-does-noise-reduction-for-speech-recognition-differ-from-noise-reduction-that | <p>this is a question that has interested me for some time now, mainly because I'm working on noise reduction for an existing speech recognition system myself.</p>
<p>Most papers on noise reduction techniques seem to focus on how to make speech more intelligible for humans, or how to improve vague terms like "speech q... | <blockquote>
<p>I don't really find papers that discuss this difference.</p>
</blockquote>
<p>There are whole books on the subject:</p>
<p><a href="https://www.microsoft.com/en-us/research/publication/robust-automatic-speech-recognition-a-bridge-to-practical-applications-1st-edition-306-pages/" rel="nofollow norefe... | 392 |
signal denoising | Why adaptive filter does not work in my application | https://dsp.stackexchange.com/questions/23229/why-adaptive-filter-does-not-work-in-my-application | <p>I got a problem when I was trying to denoise a signal. Actually, it is a simple simulation. The signal is the addition of a step signal (The info I wish to get) and a sinusoidal one (the noise I wish to remove). See below<img src="https://i.sstatic.net/NcyNr.jpg" alt="(a) The noise (b) The signal and (c) Signal + th... | <p>I tried your code change adaptfilt.lms to adaptfilt.nlms<br>
also decrease the step size to 0.0001<br>
These conditions gave me better results.<br>
nlms is better than lms as there is stability in learning filter coefficeints.The lms algorithm could change the filter coefficients drastically.</p>
| 393 |
signal denoising | Instantaneous velocity and displacement from acceleration signal using a proper filtering method | https://dsp.stackexchange.com/questions/48105/instantaneous-velocity-and-displacement-from-acceleration-signal-using-a-proper | <p>first I need to mention I'm new to signal processing. here is the situation:
I have an acceleration time-series derived from an accelerometer</p>
<p><a href="https://i.sstatic.net/rZjYW.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/rZjYW.jpg" alt="Acceleration time series"></a></p>
<p>I wanted to ... | <p>There a a number of conceptual problems with you code. The first has to do with filtering by zeroing out FFT bins. This is covered in:</p>
<p><a href="https://dsp.stackexchange.com/questions/6220/why-is-it-a-bad-idea-to-filter-by-zeroing-out-fft-bins">Why is it a bad idea to filter by zeroing out FFT bins?</a></p... | 394 |
signal denoising | How can I apply a Gabor filter to a sine waveform? | https://dsp.stackexchange.com/questions/14258/how-can-i-apply-a-gabor-filter-to-a-sine-waveform | <p>I am an ECE student, and I am doing my project on underwater communication.</p>
<p>The main concept of my project is to denoise the signal by using UFB and WPD algorithms, and giving that output to a matched filter. I have already generated the sinewave and added noise and given it to the matched filter. </p>
<p>H... | 395 | |
signal denoising | Am I generating audio signal with a given particular SNR value correctly? | https://dsp.stackexchange.com/questions/94774/am-i-generating-audio-signal-with-a-given-particular-snr-value-correctly | <p>I am using this as my reference:
<a href="https://www.mathworks.com/help/deeplearning/ug/denoise-speech-using-deep-learning-networks.html" rel="nofollow noreferrer">https://www.mathworks.com/help/deeplearning/ug/denoise-speech-using-deep-learning-networks.html</a></p>
<blockquote>
<p>Add washing machine noise to the... | <p>It appears to be correct, assuming we define SNR as the total power in the signal relative to the total power in the noise although I would proceed a little differently. To note briefly first, the SNR of actual concern may be quite different from this depending on the bandwidth of interest and the noise density with... | 396 |
signal denoising | Noise sensitivity of the (classical) Empirical Mode Decomposition routine | https://dsp.stackexchange.com/questions/61692/noise-sensitivity-of-the-classical-empirical-mode-decomposition-routine | <p>I tried to apply a MATLAB Empirical Mode Decomposition routine to denoise a signal, basically retaining only the last IMFs, with a criterion based on the mode energy.</p>
<p>To validate the routine, I have built a synthetic signal with added Gaussian noise + a sinusoidal disturbance. I noticed that the EMD routine ... | <p>Indeed, at least in my experience, computing IMFs can be sensitive to borders, impulse signals and noise realizations. As you are interested in wavelets, note that in <a href="https://doi.org/10.1109/LSP.2003.821662" rel="nofollow noreferrer">Empirical mode decomposition as a filter bank</a> a link is made with DWT... | 397 |
signal denoising | Some questions about the intuition of the DWT | https://dsp.stackexchange.com/questions/68852/some-questions-about-the-intuition-of-the-dwt | <p>Assuming a DWT of a signal of length 8 with Haar filter taps. At the lowest level, I end up with a3 and d3 both of length 1, d2 of length 2 and d1 of length 4 which is the same number of coefficients of the original signal and which I can plot on a dyadic grid.</p>
<p>In contrast to the WPT in the DWT there is only ... | <p>First, one should be cautious about processing short signals like these. I am unsure about the length of 3 for <code>a3</code> and <code>d3</code>. Now, the many questions:</p>
<ol>
<li>I would not call them "frequency plot", but stacked subband plots. They are just illustrations of the behavior of the wav... | 398 |
signal denoising | What is the best method to filter a signal where baseline and the signal of interest have overlapping frequency range? | https://dsp.stackexchange.com/questions/92054/what-is-the-best-method-to-filter-a-signal-where-baseline-and-the-signal-of-inte | <p>I am reading out the movement of a motor arm using a Hall sensor and a magnet pair. The hall sensor measures the distance between the sensor and the magnet.
The motor arm is being moved with a band-limited Gaussian white-noise signal (0-300 Hz). Due to the movement being very small, the stimulus being a white-noise,... | <p>This would be a good application for using the Cross Spectral Density between the input and output. The Cross Spectral density (which is Coherence when normalized) provides the relative magnitude and phase for the system transfer function based on the correlated components between the input noise-like signal and the... | 399 |
convolution | Convolutions with changes to the argument | https://dsp.stackexchange.com/questions/70523/convolutions-with-changes-to-the-argument | <p>I think I understand what happens when I shift the argument, but I'm not sure what should happen when the signal is compressed or expanded. In particular I'm trying to figure out what happens when the convolution where <span class="math-container">$y(t)=x(t)*h(t)$</span> is changed to <span class="math-container">$x... | <p>Let me show you how to manipulate the convolution integral.</p>
<p>Let</p>
<p><span class="math-container">$$y(t) = x(t) \star h(t) = \int_{-\infty}^{\infty} x(\tau) h(t-\tau) d\tau \tag{1} $$</span></p>
<p>Let <span class="math-container">$a > 1$</span> that we have a <em>compressed</em> signal <span class="mat... | 400 |
convolution | generator matrix coefficient in convolutional code | https://dsp.stackexchange.com/questions/72067/generator-matrix-coefficient-in-convolutional-code | <p>I cant determine a type of the following code:</p>
<pre><code>G_1=1 // g_1=1
G_2=11 // g_2=x+1
</code></pre>
<p>Accorsing to description, it is convolutional code but I dont understand the type ( code rate)?</p>
| <p>It is a <em>systematic</em> rate-<span class="math-container">$\frac 12$</span> convolutional with constraint length <span class="math-container">$2$</span>.</p>
| 401 |
convolution | Verifying the computation of a convolution | https://dsp.stackexchange.com/questions/3529/verifying-the-computation-of-a-convolution | <p>I have an input signal $$x(n)=\left(3,-5,4,3,-1,-2,6,8\right), n=-3,..,4$$ and impulse response $$h(n)=(1,-1,1,-1,1), n=-1,...,3.$$</p>
<p>The convolution between $x(n)$ and $h(n)$ is </p>
<p>$$x(n)*h(n)=\sum_{-\infty}^\infty x(k)h(n-k)$$
If I'm not mistaken, I can reduce this to the finite sum
$$=x(-3)h(n+3)+x(-... | <p>I would have liked to give a longer answer, but yes, your approach is correct. I don't see any problems with what you laid out in your question.</p>
| 402 |
convolution | Breaking a convolution into smaller pieces | https://dsp.stackexchange.com/questions/6298/breaking-a-convolution-into-smaller-pieces | <p>For a project I need to do convolution and i use gpu for calculations. Sometimes I have to deal with kernel sizes of 50x50 and this size of kernel is sufficiently large that it chokes the gpu. (not enough memory svailable by the gpu) I need to find a way to break the kernel into smaller sizes (8x8 or similar) and do... | <p>Yes, you can split them up. Convolution is a linear process, which means that <a href="http://en.wikipedia.org/wiki/Superposition_principle" rel="nofollow">superposition</a> holds. Thus, you can break up any convolution kernel $k$ into multiple parts ($k_1, k_2, ... k_N$) such that $k = \sum k_i$.</p>
<p>For exam... | 403 |
convolution | Is it meaningful to find linear convolution of just two random sequences? | https://dsp.stackexchange.com/questions/11012/is-it-meaningful-to-find-linear-convolution-of-just-two-random-sequences | <p>Could it bring any meaning? Is this kind of convolution be useful is solving anything?</p>
| <p>No, if the two sequences are random then convolving them is not useful.</p>
| 404 |
convolution | Convolution that results in an all-zero sequence | https://dsp.stackexchange.com/questions/11518/convolution-that-results-in-an-all-zero-sequence | <p>I am asked to find a pair of sequences, each one of which contains three distinct values and where the convolution is an all-zero sequence.</p>
<p>I've came to the conclusion that one of the sequences must be infinite but just can't think of any examples...</p>
| <p>thanks for the input. I found a simple solution: </p>
<p>sequence A: {...1,0,-1,0,1,0,-1,0...} (i.e. 1,0,-1,0 periodic) </p>
<p>and</p>
<p>sequence B: {0,x,y,x,y,0}</p>
| 405 |
convolution | Convolution from bottom right | https://dsp.stackexchange.com/questions/16232/convolution-from-bottom-right | <p>I want to do a convolution from the bottom right and not as usual from the top left. I think conv2 of Matlab only does from the top left.</p>
<p>How can I do a convolution in Matlab from the bottom right?</p>
<p>Thank you very much for the answers.</p>
| <p>I hope I understand your question correctly, in that you're trying to produce a mirror image of the convolution kernel (filter) and then convolve. Flip you convolution kernel. In MATLAB, you can use the <code>flip</code> command. If you flip it left-to-right, this should do it.</p>
<p>However, if you're simply sayi... | 406 |
convolution | Convolution equivalent to matrix multiplication? | https://dsp.stackexchange.com/questions/26176/convolution-equivalent-to-matrix-multiplication | <p>Is it possible to write the full convolution between the image and the filter as a matrix multiplication operation? If so, can someone give a simple example of how that works?</p>
| 407 | |
convolution | Can you present the convolution of sinusoidal with itself? | https://dsp.stackexchange.com/questions/27154/can-you-present-the-convolution-of-sinusoidal-with-itself | <p>Ladies, Gentlemen,
Because I am homeless (in France), and get internet access only in public libraries with many restrictions in timing etc, I can not write down even a simple convolution. So I ask you post here the convolution of some sinusoidal function with itshelf. </p>
<p>For example: 0.951056516295, 0.58778... | <p>For your data points I get:</p>
<blockquote>
<p>-2.467162e-16 -9.045085e-01 -1.118034e+00 7.725425e-01 2.500000e+00 7.725425e-01 -1.118034e+00 -9.045085e-01 -1.480297e-16</p>
</blockquote>
<p>from</p>
<pre><code>#27154
data <- c(0.951056516295, 0.587785252292, -0.587785252292, -0.951056516295, 0.)
ou... | 408 |
convolution | Is output of convolution of sinusoidal with itself, also sinusoidal? | https://dsp.stackexchange.com/questions/27161/is-output-of-convolution-of-sinusoidal-with-itself-also-sinusoidal | <p>Ladies, Gentlemen, </p>
<p>In my last question I asked you present the convolution of sinusoidal with itself. I accept Mr Peter K.'s answer. Now my question is much more important. Is output of convolution of sinusoidal with itself, also sinusoidal? </p>
<p>Regards </p>
| 409 | |
convolution | What does convolution has the meaning? | https://dsp.stackexchange.com/questions/29594/what-does-convolution-has-the-meaning | <p>As I know, if we want to know the LTI system output, then we do convolution between input x[n] and impulse response h[n].
but actually,in this question, I want to know what does convolution has the behind meaning. </p>
<p>Why do we do convolution(sum of products) not just using adder or multiplier for calculation b... | <p>I explained in <a href="https://en.wikipedia.org/wiki/Talk:Convolution#Why_the_time_inversion.3F" rel="nofollow noreferrer">"Why is time inversion?"</a></p>
<p><a href="https://i.sstatic.net/WdcEZ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/WdcEZ.png" alt="enter image description here"></a></p>
... | 410 |
convolution | Minimal number of additions in convolution | https://dsp.stackexchange.com/questions/42618/minimal-number-of-additions-in-convolution | <p>The Winnograd algorithm can be used to reduce the number of multiplications in convolution. Is there a known method of reducing the number of additions in convolution?</p>
| <p>One method which attracted my attention recently is <a href="http://www.rle.mit.edu/dspg/documents/Discrete-TimeRandom.pdf" rel="nofollow noreferrer">Discrete Time Random Sampling</a>.</p>
<p>Which is an approximation method useful to reduce both multiplications and additions in filtering. </p>
<p>Filter and $N$-l... | 411 |
convolution | Impulse response time period in circular convolution | https://dsp.stackexchange.com/questions/44584/impulse-response-time-period-in-circular-convolution | <p>While considering an input to be periodic of Period N, can the impulse response not be periodic of period greater than N ? If it can be, how can one compute it’s convolution?</p>
| <p>Circular convolution assumes that all signals ($x[n]$, $h[n]$ and $y[n]$) are periodic in the same integer $L$. When any of the signals are shorther than $L$ then they are padded with enough zeros to make them periodic with $L$. When $x$ or $h$ has a period larger than $L$ then there will be <strong>aliasing</strong... | 412 |
convolution | Where does convolution fit into tracking fluorescent photons using MC models? | https://dsp.stackexchange.com/questions/45175/where-does-convolution-fit-into-tracking-fluorescent-photons-using-mc-models | <p>I have been reading this old paper by Steven Jacques, a titan in the world of using Monte-Carlo methods for photon propagation and distributions.</p>
<p><a href="https://www.osapublishing.org/ao/abstract.cfm?uri=ao-28-20-4286" rel="nofollow noreferrer">https://www.osapublishing.org/ao/abstract.cfm?uri=ao-28-20-4286... | 413 | |
convolution | Linear convolution of discrete signals with defined lengths | https://dsp.stackexchange.com/questions/45503/linear-convolution-of-discrete-signals-with-defined-lengths | <p>What is the maximum count of non-zero elements, that can a linear convolution of discrete signals of "lengths" 5 and 7 have?</p>
<p>When I label the length of signal $x[n]$ as $M$, and the length of
signal $h[n]$ as $N$, then the length of their convolution is the signal $y[n]=M+N-1$. However this is not that thing... | <p>It seems like you have already the correct answer, but try to visualize what's going on</p>
<p>First understand that signals of length $n_0$ are really infinite length, but have nonzero values at $n = 0$ and $n = n_0 - 1$. The values in between can be anything, but for the purposes of this problem take them to be n... | 414 |
convolution | Convolution Sum | https://dsp.stackexchange.com/questions/49519/convolution-sum | <p>I understand convolution is linear combination of delayed impulses of decomposed signal.</p>
<p>$$\int_{-\infty}^{+\infty} x(\tau)h(t-\tau)\mathrm{d}\tau = g(t)$$</p>
<p>I want to know about these decomposed signals.</p>
<p>If I have my $g(t)$, can I decompose it in different ways?
If yes what are those few dec... | <p>I'm afraid you <em>don't understand convolution</em></p>
<p>Let,<br>
$x(t)$ : <code>[1 2 3 4]</code><br>
$h(t)$ : <code>[1 2]</code></p>
<p>Your <code>decomposed signals</code> are now<br>
<code>[1 0 0 0]</code><br>
<code>[0 2 0 0]</code><br>
<code>[0 0 3 0]</code><br>
<code>[0 0 0 4]</code> </p>
<p>If you were ... | 415 |
convolution | Graphical method for convolution? | https://dsp.stackexchange.com/questions/52414/graphical-method-for-convolution | <p>Is graphical method the best way to solve convolution questions whether they be discrete or continuous?</p>
<p>I was given a question:</p>
<p><span class="math-container">$$x[n]=1$$</span> <span class="math-container">$$0\leq n \leq 4 $$</span></p>
<p><span class="math-container">$$h[n]=\alpha^n$$</span> <span ... | <p>Graphical evaluation of convolution (flip n drag) is a very useful, helpful and indipensible method which aids in a very quick visual anticipation of the output, in terms of the input sequences. Indeed even if you don't use specifically the graphical method, you would still benefit from drawing a plot of input seque... | 416 |
convolution | Circular convolution of a non causal signal | https://dsp.stackexchange.com/questions/53955/circular-convolution-of-a-non-causal-signal | <p>I know how we compute the <span class="math-container">$N$</span> point circular convolution of a two causal signals, but what about a signal such as <span class="math-container">$\{1,-1,2,1\}$</span> where, the position of 2 is the <span class="math-container">$0^{th}$</span> index and the other sequence is <span c... | <p>For an <span class="math-container">$N$</span>-point circular convolution you can think of each signal as being periodically extended with period <span class="math-container">$N$</span>. For your example with <span class="math-container">$N=4$</span> that would mean that the two sequences are</p>
<p><code>2 1 1 -1<... | 417 |
convolution | Impulse response convolution and normalization2 | https://dsp.stackexchange.com/questions/58896/impulse-response-convolution-and-normalization2 | <p>when I take inverse Laplace transform of a system transfer function \</p>
<p>Lets say LPF whose TF is </p>
<p><span class="math-container">$$\frac{Y(s)}{X(s)} \triangleq H(s) = \frac{W}{s+W} $$</span></p>
<p>the inverse Laplace/impulse response is </p>
<p><span class="math-container">$$h(t) = We^{-Wt}u(t) $$</sp... | <p>I think you're likely forgetting how the anti-derivative of <span class="math-container">$h(t)$</span> affects the gain of the convolution operation. Recall that somewhere in your convolution integral, you'll be taking an integral of the form <span class="math-container">$\int We^{W\tau} d\tau$</span>. The Chain R... | 418 |
convolution | Convolution of $f(2x)$ and $g(3x)$ | https://dsp.stackexchange.com/questions/35479/convolution-of-f2x-and-g3x | <p>As I know, convolution is defined as $f(x)*g(x) = \int_{-\infty}^{+\infty}f(\tau)g(x-\tau)d_{\tau}$, but what if we want to convolve $f(2x)$ and $g(3x)$? It should be like $f(2x)*g(3x) = \int_{-\infty}^{+\infty}f(2\tau)g(3x-\tau)d_{\tau}$ or $f(2x)*g(3x) = \int_{-\infty}^{+\infty}f(2\tau)g(3x-3\tau)d_{\tau}$ or anyt... | <p>Replace $x$ by $x - \tau$ . So option b i.e $3x-3\tau$.</p>
| 419 |
convolution | How to take the linear convolution of these two signals? | https://dsp.stackexchange.com/questions/35736/how-to-take-the-linear-convolution-of-these-two-signals | <p>How do I perform the linear convolution of the following two signals? I am having trouble relating $x[n]$ to a series of points, like was given by $h[n]$ below.</p>
<p>$$x[n] = e^{j\pi n}\left\{{u[n]}-u[n-8]\right\}\quad\text{and}\quad h[n] = (-1)^{n}\left\{{u[n]}-u[n-4]\right\}$$</p>
<p>$x[n]$ is a finite-length... | <p>For $n = 1\ldots 8$
$$x[n] = e^{j\pi n}\{{u[n]}-u[n-8]\} = (-1)^{n}$$
and for $n = 0\ldots 3$
$$h[n] = (-1)^n$$
Else, if $n > 8$ or $n < 1$, then $x[n] = 0$. Similarly, if $n < 0$ and $n > 3$ then $h[n] = 0$. Using the definition of convolution,
$$y[k] =(h * x)[k] = \sum\limits_{m = 0}^3 h[m]x[k-m] $$
... | 420 |
convolution | Variance of zero-mean signal after convolution for SIR computation | https://dsp.stackexchange.com/questions/62619/variance-of-zero-mean-signal-after-convolution-for-sir-computation | <p>my goal is to scale desired, interfering signal at the receiver in order to achieve desired SIR (signal to interference ratio) for beamforming (source separation) application.</p>
<p>Let be:</p>
<ul>
<li><span class="math-container">$s(t)$</span> a known speech signal with zero mean <span class="math-container">$\... | 421 | |
convolution | What does shift and multiply-accumulate mean in terms of Convolutional Neural Networks? | https://dsp.stackexchange.com/questions/78079/what-does-shift-and-multiply-accumulate-mean-in-terms-of-convolutional-neural-ne | <p>While reading this <a href="https://arxiv.org/pdf/1811.08383.pdf" rel="nofollow noreferrer">paper</a>, I came across the following paragraph -</p>
<p>"Our intuition is: the convolution operation consists of shift and multiply-accumulate.
We shift in the time dimension by ±1 and fold the multiply-accumulate from... | 422 | |
convolution | Convolution problem | https://dsp.stackexchange.com/questions/32447/convolution-problem | <p>This will be maybe quite easy fore somebody but I am not sure how to solve it. If I have a signal which is equal to</p>
<p>$$
y(n)=x(n)\star g(n), \quad n\in[0,1,...,N]
$$
where $\star$ is convolution operator, how do I get expression for taking every $K^{\textrm{th}}$ sample of $y(n)$, i.e., $y(Kn)$?</p>
| <blockquote>
<p>how do I get expression for taking every Kth sample of y(n), i.e., y(Kn)?</p>
</blockquote>
<p>What I understand from this is you want a <strong>notation</strong> that represents $y[Kn]$ as a <strong>convolution</strong> operator. That doesn't exist. Or I cant remember.</p>
<p>For example the notati... | 423 |
convolution | the sub-range of circular and linear convolution | https://dsp.stackexchange.com/questions/37107/the-sub-range-of-circular-and-linear-convolution | <p>circular convolution $x_{_3p}[n]$ = $x_1[n]~\circledast_N ~x_2[n]$</p>
<p>is a period version of the linear convolution $x_{_3p}[n]=x_1[n] * x_2[n]$ </p>
<p>The length of $x_1[n]$ and $x_2[n]$ are $L$ ($n\in[0,\ldots,L-1]$) and $P$ ($n\in[0,\ldots,P-1]$) points, respectively.</p>
<p>The minimum value of $N$ tha... | <p>Given an <span class="math-container">$L_x$</span>-point discrete-time sequence <span class="math-container">$x[n]$</span>, nonzero for the range <span class="math-container">$0 \leq n < L_x$</span>, and <span class="math-container">$L_y$</span>-point sequence <span class="math-container">$y[n]$</span>, nonzero f... | 424 |
convolution | Why does convolution reverb work? | https://dsp.stackexchange.com/questions/79604/why-does-convolution-reverb-work | <p>I've just begun learning about signal processing on my own, and after reading about convolution I'm curious about <em>why</em> convolution reverb works. That is given a recorded impulse <span class="math-container">$\hat{f}$</span> and an audio signal <span class="math-container">$g$</span>, why does the convolution... | <p>A room consists of many hard surfaces. When you generate a wideband click sound in that room («perturbations about the mean pressure»), those waves will travel into the room, be reflected by surfaces, travel once more, be re-reflected etc. As time goes by, the wave tends to diminish due to spherical expansion, and b... | 425 |
convolution | Plot the sum frequency generation spectrum using convolution MATLAB | https://dsp.stackexchange.com/questions/80989/plot-the-sum-frequency-generation-spectrum-using-convolution-matlab | <p>I am attempting to calculate the spectrum of a pulse that has undergone sum-frequency generation (in this case it is a gaussian, so it is correct to also say frequency doubling/Second harmonic generation). The SHG signal in the frequency domain is given as,</p>
<p><span class="math-container">$$E_{SHG}(2\omega) = E_... | <p>You have a gaussian centered at 500 THz. We would expect the convolution to have a single gaussian centered at 1000 THz.</p>
<p>A linear convolution of two sequences of N points each will have a length of 2*N-1 samples. You have the added complication that your frequency vectors don't start at 0Hz. One way to fix th... | 426 |
convolution | The proof of the dual convolution/multiplication properties? | https://dsp.stackexchange.com/questions/53921/the-proof-of-the-dual-convolution-multiplication-properties | <p>I've been trying to find a rigorous proof of the dual convolution / multiplication, but I found nothing, can you give me a hand with this?</p>
<p><span class="math-container">\begin{align}
f(t) * g(t) &\overset{\mathcal F}{\iff} F(j\omega)G(j\omega)\\
f(t)g(t) &\overset{\mathcal F}{\iff}\frac1{2\pi} F(j\ome... | <p>Just do the double integration:</p>
<p><span class="math-container">$$\begin{align*}\mathscr{F}\left\{f(t) * g(t)\right\} &= \mathscr{F}\left\{\int_{-\infty}^\infty f(\tau)g(t-\tau)d\tau\right\} \\
\\
&= \int_{-\infty}^\infty\left[\int_{-\infty}^\infty f(\tau)g(t-\tau)d\tau\right]e^{-j\omega t}dt\\
\\
&... | 427 |
convolution | Convolving two signals | https://dsp.stackexchange.com/questions/3045/convolving-two-signals | <p>I saw a video where this guy used a program to do a frequency analysis on a voice signal and a sawtooth wave (I'm assuming this was FFT). Then he saved the plots as images and combined them pixel by pixel through multiplication using photoshop. He then put this picture back into the program and it did the inverse tr... | <p>From your description, here is what is happening in the video:</p>
<ul>
<li>The short-term Fourier transform (aka spectrogram) of the signals is computed. The output of this operation is a matrix of complex values, which cannot be represented as images. Thus, the magnitude or the square of the magnitude is extracte... | 428 |
convolution | What type of circuit is responsible for convolution in the classic analog telephone? | https://dsp.stackexchange.com/questions/2891/what-type-of-circuit-is-responsible-for-convolution-in-the-classic-analog-teleph | <p>I'm interested in learning how telephones work, so I did a little bit of reading about signal processing. When I came up with the word convolution, I quickly realized the importance of this term.</p>
<p>To begin with, I want to know how classic analog telephones worked. The apparent simplicity of their design appea... | <p>Convolution is a mathematical abstraction describing how a linear, time-invariant system affects a signal going through it.</p>
<p>Sometimes one explicitly designs a system to convolve a signal by a predefined impulse response (for example when building a digital filter); but more often than not, convolution is use... | 429 |
convolution | Can two nonzero signals $x[n]$ and $y[n]$ give a zero convolution | https://dsp.stackexchange.com/questions/11262/can-two-nonzero-signals-xn-and-yn-give-a-zero-convolution | <p>Suppose $x[n]$ and $y[n]$ are two nonzero signals(i.e., $x[n] \neq 0$ for at least one value of n and similarly for $y[n]$).Can the convolution between $x[n]$ and $y[n]$ result in an identically zero signal? In other words, is it possible that $\displaystyle\sum_{k = -\infty}^{k = +\infty}x[k]y[n-k] = 0$ for all n.... | <p>Yes, for example let</p>
<p>$$x[k]=1$$</p>
<p>for all $k$ and</p>
<p>$$y[k] = \begin{cases}1 & k=0\\-1 & k=1\\0 & otherwise \end{cases}$$</p>
<p>It is easy to see that in case of a convolution, the result will be zero for all values of $n$.</p>
| 430 |
convolution | Basic question: Why is the output of a system the convolution between the impulse response and the input? | https://dsp.stackexchange.com/questions/20455/basic-question-why-is-the-output-of-a-system-the-convolution-between-the-impuls | <p>I forgot a very simple fact and I am now struggling to find reference that proves this basic property?</p>
<p>How would you prove that for a single in single out system, the system output is the impulse response convoluted with the input?</p>
| <p>Because it is the response of the system when an unit impulse (delta function) is applied to the input of the system. So basically, If you multiply this output impulse response of the system to each of the input samples and then add them all, you get the overall output of the system. And this is only true, If the s... | 431 |
convolution | How can I calculate the cyclic (periodic) convolution? | https://dsp.stackexchange.com/questions/7979/how-can-i-calculate-the-cyclic-periodic-convolution | <p>I'd like to understand how to calculate the cyclic convolution as well as understand what that means exactly. How should I go about finding the output for various periods for a system?</p>
<p>I have an example: </p>
<p>$$
x(n) =
\begin{cases}
n & \textrm{for} \quad 1 \leq n \leq 3\\ 0 &\textrm{otherwise}\... | <p>People generally define the cyclic convolution of <em>periodic</em> sequences
$x$ and $h$ of period $N$ as
$$y[n] = \sum_{m=0}^{N-1}x[m]h[n-m], n = 0, 1, \ldots, N-1.\tag{1}$$
Note that the above expression consists of $N$ different sums that
you have to compute, and if while computing any particular sum,
the value ... | 432 |
convolution | Applications or physical interpretation of auto-convolution? | https://dsp.stackexchange.com/questions/22463/applications-or-physical-interpretation-of-auto-convolution | <p>I wonder if anyone has any experience with auto-convolution. In particular i'm interested in understanding the physical interpretation of it.
I understand what convolution, correlation and auto-correlation are, also i'm aware that the definition of auto-convolution will be something like
$$f\ast f = \int_{-\infty}^... | <p>Autoconvolution is used in signal detection, but the way you've written it is not correct. Suppose you're trying to detect a signal $f(t)$ by filtering with h(t).</p>
<p>$y(t) = f(t) \ast h(t)$</p>
<p>You want to maximize your response to the signal $f(t)$. We can do this by maximizing the correlation coefficient ... | 433 |
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