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adaptive filtering | LMS adaptive filter relatively delayed signal and reference inputs | https://dsp.stackexchange.com/questions/26664/lms-adaptive-filter-relatively-delayed-signal-and-reference-inputs | <p>I'm using two microcontrollers to implement an adaptive LMS filter to filter out the noise from the signal. One is recording the noise and streaming the data to the other microcontroller which is recording the (noised) signal and using the noise reference, filtering it out.</p>
<p>How does the delay between those s... | <p>The adaptive filter tries to emulate the assumed filtering process between the noise reference signal and the actual noise in the noisy signal. </p>
<p>If $n(t)$ is the actual noise in the noisy signal, and $n_r(t)$ is the noise reference, it is assumed that there's a linear filtering relationship between the two:<... | 834 |
adaptive filtering | MATLAB model for equalizer using LMS algorithm adaptive filter and unexpected output curve | https://dsp.stackexchange.com/questions/72047/matlab-model-for-equalizer-using-lms-algorithm-adaptive-filter-and-unexpected-ou | <p>The MATLAB code below is for equalizer using lms algorithm adaptive filter and then plotting MSE (Mean Square Error) Vs Iteration numbers</p>
<hr />
<pre><code>%% Channel Equalization using Least Mean Square (LMS) algorithm
% Author: SHUJAAT KHAN
clc;clear all;close all;
%% Channel and noise level
h = [0.9 0.3 0.5 -... | 835 | |
adaptive filtering | Can a LMS adaptive filter be adapted for MISO? | https://dsp.stackexchange.com/questions/84076/can-a-lms-adaptive-filter-be-adapted-for-miso | <p>How would the LMS equalizer dimensions change for the MISO case?</p>
<p>LMS adaptive filters are typically described for equalizing a single input signal, <span class="math-container">$x(t)$</span>. Can the LMS algorithm be modified in the MISO case to perform diversity combining when the transmitter has <span class... | <p>I'm surprised I couldn't find a decent reference for this on the web.</p>
<p>Terminology gets difficult. Let <span class="math-container">$s(n)$</span> (a scalar) be the transmitted information. Let there be <span class="math-container">$M$</span> inputs. Let <span class="math-container">$\mathbf r(n)$</span> be ... | 836 |
adaptive filtering | Updating forgetting factor in un-normalized lattice recursive least squares adaptive filter | https://dsp.stackexchange.com/questions/61544/updating-forgetting-factor-in-un-normalized-lattice-recursive-least-squares-adap | <p>The algorithms given for <a href="https://en.wikipedia.org/wiki/Recursive_least_squares_filter#Lattice_recursive_least_squares_filter_(LRLS)" rel="nofollow noreferrer">un-normalized LRLS</a> and <a href="https://en.wikipedia.org/wiki/Recursive_least_squares_filter#Normalized_lattice_recursive_least_squares_filter_(N... | 837 | |
adaptive filtering | Adaptive filter to scale and phase shift two sensors output | https://dsp.stackexchange.com/questions/49221/adaptive-filter-to-scale-and-phase-shift-two-sensors-output | <p>One way of separating downgoing and upgoing wavefields in offshore seimic processing is to add signals from hydrophone and vertical component of the geophone (they are co-located). Hydrophone only registers a change in the pressure whereas geohphone as well as registering a change in seismic field also reacts to the... | <p>It seems that you want to equalize one time series to the other or vice versa or some combination. The general problem is then (in shorthand)
$$
h_1{\Large *}y_1 \approx h_2{\Large *}y_2
$$
where $\Large *$ denotes convolution, $h_i$ are filters, and $y_i$ are your time series. If you simply equalize one time series... | 838 |
adaptive filtering | RLS adaptive filter intuitive explanation of the so-called desired signal | https://dsp.stackexchange.com/questions/94203/rls-adaptive-filter-intuitive-explanation-of-the-so-called-desired-signal | <p>This wikipedia page <a href="https://en.wikipedia.org/wiki/Recursive_least_squares_filter" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Recursive_least_squares_filter</a> (and in fact other sources) do not explain the apparent paradox of the cost function that computes the MSE of the output and the "... | <p>A good example of an adaptive filter is an Acoustic Echo Canceller as shown in this <a href="https://www.researchgate.net/profile/Mirco-Ravanelli-2/publication/275637439/figure/fig2/AS:614318697619469@1523476399262/Principle-of-acoustic-echo-cancellation-x-is-the-known-signal-emitted-by-a-loudspeaker.png" rel="nofol... | 839 |
adaptive filtering | Regression vector size for prediction, reconstruction and filtration with adaptive filters | https://dsp.stackexchange.com/questions/37855/regression-vector-size-for-prediction-reconstruction-and-filtration-with-adapti | <p>I am working with adaptive filters and similar adaptive models (mainly with gradient adaptation) for a few years. I and my colleagues always struggle to find out the correct size of regression vector.</p>
<p>So far, as I find out by the hard way (experience):</p>
<ol>
<li><p>for filtration mostly works well (low M... | <p>Suppose that you are adapting <span class="math-container">$w$</span> to minimize <span class="math-container">$\text{E}(y[n]-w[n]*u[n])^2$</span> where
<span class="math-container">$$y[n]=h[n]*u[n]+\nu[n]$$</span>
<span class="math-container">$y[n]$</span> and <span class="math-container">$u[n]$</span> are known an... | 840 |
adaptive filtering | Unknown symbol/expression in text about adaptive filters (cst) | https://dsp.stackexchange.com/questions/59715/unknown-symbol-expression-in-text-about-adaptive-filters-cst | <p>I am currently reading a chapter about adaptive filters from the <a href="https://link.springer.com/book/10.1007/978-3-540-49127-9" rel="nofollow noreferrer">Springer Handbook of Speech Processing</a>. </p>
<p>In a formulation of the variable stepsize normalized least mean squares (VSS-NLMS)-algorithm, i found an e... | <p>The standard normalized step-size LMS algorithm computes the current step-size according to</p>
<p><span class="math-container">$$ \mu = \frac{c}{s_k^T \cdot s_k} $$</span></p>
<p>where <span class="math-container">$c$</span> is a suitable scale factor and <span class="math-container">$s_k^T \cdot s_k$</span> is ... | 841 |
adaptive filtering | Is there a widely available implementation of an adaptive, recursive, numerically stable IIR filter? | https://dsp.stackexchange.com/questions/19125/is-there-a-widely-available-implementation-of-an-adaptive-recursive-numericall | <p>I need to identify the coefficients of a linear, causal, time-invariant physical system that can be described by a classical state-space formulation.</p>
<p>For the sake of the example, suppose that the system has two states, only one of which is observed, and one input. Suppose that this state-space is described b... | <p>While I may not be the final authority, I have looked into this. In short, no. </p>
<p>From my own research, the problem is stability. When the filter is extended to have a wider bandwidth, which of course means that the y[n] values and lags 'move quickly', and then is quenched to a lower bandwidth, where the y[n] ... | 842 |
adaptive filtering | Adaptive filter for noise cancellation when measuring some input | https://dsp.stackexchange.com/questions/54660/adaptive-filter-for-noise-cancellation-when-measuring-some-input | <p>The context is as follows: I want to measure (as in, digitize) some input signal <span class="math-container">$x$</span> (I have no detailed knowledge about <span class="math-container">$x$</span> or its statistical description).</p>
<p>A noise signal <span class="math-container">$x_N$</span> contaminates <span cl... | <p>I'm a little skeptical of your derivation and notation as it abstains from telling whether a Mean-Square or a Least-Squares metric of error is minimized, but rather just works on an instantaneous error at sample <span class="math-container">$n$</span>. But I believe you eventually would devise an LMS or RLS filter, ... | 843 |
adaptive filtering | Seperation of wideband and narrowband - Adaptive Filter | https://dsp.stackexchange.com/questions/54079/seperation-of-wideband-and-narrowband-adaptive-filter | <p>I have the following diagram for the adaptive seperation of a narrowband and wideband signal using LMS algorithim,</p>
<p><a href="https://i.sstatic.net/IZCIN.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/IZCIN.png" alt="enter image description here"></a></p>
<p>The way it was explained to us was ... | <p>A narrowband signal seems like (almost) periodic as indicated by</p>
<p><span class="math-container">$$ x[n] = m[n] \sin( w_0 n) $$</span> where the message <span class="math-container">$m[n]$</span> has such a low bandwidth that the peak amplitude (the <strong>envelope</strong>) of the carrier sine wave changes ve... | 844 |
adaptive filtering | LMS adaptive filter noise suppression- question about my implementation | https://dsp.stackexchange.com/questions/55723/lms-adaptive-filter-noise-suppression-question-about-my-implementation | <p>I am writing LMS filter to suppress noise in wav file (I know there are many modules to do this but I need to write LMS manually now as I will translate it into C later).</p>
<p>According to this answer[1], the inputs will be the noisy voice and a shifted version of it
here is my python code:</p>
<pre><code>import... | 845 | |
adaptive filtering | IIR Adaptive Filter in MATLAB | https://dsp.stackexchange.com/questions/71770/iir-adaptive-filter-in-matlab | <p>Suppose I have a IIR filter represented by <span class="math-container">$$G_0\left(z\right)=\frac{1}{1-0.2z^{-1}-0.1z^{-2}}$$</span></p>
<p>I would like to use the LMS algorithm to model an FIR filter <span class="math-container">$G\left(z\right)$</span> of order <span class="math-container">$N = 15$</span> such tha... | <p>An adaptive FIR filter is a FIR filter, that uses some kind of an adaptive algorithm to change the filter weights and reach a desired state. In case of using an LMS algorithm the general update equation is the following:</p>
<p><span class="math-container">$$
\mathbf{w}(n+1) = \mathbf{w}(n) + \mu\cdot e(n) \cdot \ma... | 846 |
adaptive filtering | Problem with Feedback in LMS adaptive filter for ANC | https://dsp.stackexchange.com/questions/96618/problem-with-feedback-in-lms-adaptive-filter-for-anc | <p>I am attempting to make ANC headphones, so far I have constructed the headphones and validated that every component works. I have also constructed an FIR adaptive filter using leaky NLMS for its algorithm. I have validated that this filter works by using the signal from the headphones reference microphone as its inp... | 847 | |
adaptive filtering | Upsampled input to an Adaptive filter? | https://dsp.stackexchange.com/questions/37074/upsampled-input-to-an-adaptive-filter | <p>I will try to explain the issue I am having as clearly as possible without going into my coding or maths. I have my own and a MATLAB Central implementation pf standard LMS in MATLAB. Fixed step size. No normalization or other stuff.</p>
<p>I am trying to use it in a system identification setup. I generate a vector ... | <p>Prior to upsampling, you have a white signal meaning every single frequency in the Nyquist bandwidth from $-\pi$ to $\pi$ is represented. This is a requirement to obtain an impulse (because the Fourier transform of an impulse is a white spectrum). The reason that white signals are often used as inputs for purposes o... | 848 |
adaptive filtering | Spline-Based Adaptive Interpolation Filters? | https://dsp.stackexchange.com/questions/38568/spline-based-adaptive-interpolation-filters | <p>My understanding of interpolation specific to resampling applications is limited to the concept of inserting zeros, then designing a filter to minimize distortion in the passband and reject the images the zero-insert creates (to desired performance levels), such as what is depicted in a simple interpolate by 4 zero-... | <p>Look up "Farrow filter". It's essential a set of piecewise polynomial interpolators for the coefficients of an even longer (better) FIR interpolation filter (and without the need for a huge polyphase table). IIRC, it can be implemented in a straightforward arithmetic hardware pipeline (thus is likely quite suitable... | 849 |
adaptive filtering | Explain the Adaptive Part of Adaptive Algorithms - Kalman Filter and Least Mean Square / Constant Modulus | https://dsp.stackexchange.com/questions/42710/explain-the-adaptive-part-of-adaptive-algorithms-kalman-filter-and-least-mean | <p>General questions:</p>
<ul>
<li>Is the Kalman filter (they have used Unscented Kalman Filter) adaptive or not? Is the Unscented Kalman Filter used in the paper an adaptive algorithm? </li>
<li>Adaptive algorithms such as Constant Modulus and Least Squares are adaptive. Why? What is being adapted ? Based on my under... | <p>Adaptive Filters are called "Adaptive" when they can adapt to changes in data.<br>
In the filters you mentioned above, which are part of the Linear Filters family the property means their coefficients are changing over time.</p>
<p>Linear Filters are basically weighing and summing the data.<br>
For instance, given ... | 850 |
adaptive filtering | Modeling end-blown flute instrument using adaptive filter | https://dsp.stackexchange.com/questions/88123/modeling-end-blown-flute-instrument-using-adaptive-filter | <p>I want to find the resonant frequency of specific <a href="https://en.wikipedia.org/wiki/End-blown_flute" rel="nofollow noreferrer">end-blown flute</a> called <a href="http://persianney.com/technique.html" rel="nofollow noreferrer">Persian ney</a>, Using LMS in arrangement of system identification. Two signal is nee... | <p>I'm partially going on my own knowledge of electronic circuits, my own experience singing and playing (and playing with) wind instruments, and <a href="https://newt.phys.unsw.edu.au/jw/fluteacoustics.html" rel="nofollow noreferrer">this page</a>.</p>
<p>Your model is wrong (sorry).</p>
<p>A better model for a flute ... | 851 |
adaptive filtering | LMS Adaptive Filter for system identification | https://dsp.stackexchange.com/questions/85113/lms-adaptive-filter-for-system-identification | <p>i am currently attempting system identification using the LMS algorithm. The input and the output data are available and are very noisy and consists of multiple frequencies. The input and the output data are shown below.
<a href="https://i.sstatic.net/rNeKT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.... | <p>In general for a standard LMS you can only ensure convergence if the stepsize <span class="math-container">$µ < 1 / (2p\sigma^2)$</span> . With p being the filter order and <span class="math-container">$\sigma^2$</span> the variance of the input signal x. Therefore if you first low-pass filter your signal, the va... | 852 |
adaptive filtering | Recursive Least Square Adaptive Linear Equalizer | https://dsp.stackexchange.com/questions/51200/recursive-least-square-adaptive-linear-equalizer | <p>For the adaptive filter to work properly, a desired signal d(n) needs to be provided. The output from the equalizer y(n) is subtracted from d(n) to produce an error signal, which is used to adjust the filter weights.</p>
<ol>
<li><p>The adaptive filter is located on the receiver side, so how to obtain the desired s... | <p>To answer (1) the adaptive equalizer without a training sequence (blind equalization) can be used based on the decisions of the received sequence. This specifically is called a "decision directed equalizer". Of course it can not work in very low SNR conditions, where a training sequence would be required. A typical ... | 853 |
adaptive filtering | Adaptive Line noise removal using IIR notch filters | https://dsp.stackexchange.com/questions/19612/adaptive-line-noise-removal-using-iir-notch-filters | <p>I'm trying to filter out line noise(60Hz and 120Hz) from a EEG signals received over a bluetooth link. I'm proposing to use a IIR notch filter to filter out the line-noise which varies w.r.t to distance between the bluetooth transmitter and receiver. I'm not able to establish a clear relationship between the Notch f... | 854 | |
adaptive filtering | Signal chain for voice calls including adaptive noise cancellation, adaptive echo cancellation, and automatic gain control and their algorithms | https://dsp.stackexchange.com/questions/43222/signal-chain-for-voice-calls-including-adaptive-noise-cancellation-adaptive-ech | <p>I am trying to understand the entire signal chain and all the algorithms associated with adaptive filtering as mentioned in the case above. From my understanding:</p>
<ul>
<li><p><strong>Adaptive noise filtering (ANF)</strong>- can be performed with the help of Weiner filters, wavelet packet based auditory masking ... | 855 | |
adaptive filtering | Terminologies: Adaptive, recursive and iterative | https://dsp.stackexchange.com/questions/26860/terminologies-adaptive-recursive-and-iterative | <ol>
<li><p>Considering non-linear filtering technique like Extended Kalman filtering with Expectation Maximization (EM). EM is an iterative technique but what is Kalman filtering? Is Kalman Filtering called iterative approach? </p></li>
<li><p>Adaptive signal processing algorithms like Least Mean Square and Recursive ... | <blockquote>
<p>Q1: In short, is adaptive=recursive=iterative?</p>
</blockquote>
<p>Filtering is applying a filter $f$ to an input signal $x$ to get an output signal $y$:</p>
<p>$$
y(t) = f(x(t), t)
$$</p>
<p>The filter $f$ is called <a href="https://en.wikipedia.org/wiki/Iteration" rel="nofollow"><strong><em>iter... | 856 |
adaptive filtering | Adaptive Gaussian Filter for Image Denoising | https://dsp.stackexchange.com/questions/16326/adaptive-gaussian-filter-for-image-denoising | <p>I am looking for methods to enhance noisy images, where:</p>
<ul>
<li>some pixels in the image are very noise,</li>
<li>some other pixels do not contain so much noise. </li>
</ul>
<p>My first thought is to build an adaptive Gaussian filter.
This means that the Gaussian kernel will depend on the (estimated) noise ... | <p>So if I understand your description correctly your data looks something like this:</p>
<p><img src="https://i.sstatic.net/JMStt.png" alt="enter image description here"></p>
<p>In this case you could try using a robust Gaussian smoothing. This involves an extra weight term to discard 'outliers'. There are many poss... | 857 |
adaptive filtering | What's the advantage of adaptive IIR filter against FIR? | https://dsp.stackexchange.com/questions/32129/whats-the-advantage-of-adaptive-iir-filter-against-fir | <p>Adaptive IIR filters is not straightforward, and may be unstable. Many people say that adaptive IIR filters <em>use less coefficients</em> than FIR filters. What I'm curious about is how many coefficients can IIR save?</p>
<p>I tried to use adaptive IIR filters to estimate transfer function of a 32-order FIR filter... | <p>These are the key differences between FIR and IIR filters, regarding the feature you wish to control are the following:</p>
<p>$$
\begin{array}{c|lcr}
\text{Feature} & \text{IIR} & \text{FIR} \\
\hline
\text{Implementation} & \text{Poles & Zeros} & \text{Zeros Only} \\
\text{States} & \text{... | 858 |
adaptive filtering | RLS Adaptive Filter for estimating signal | https://dsp.stackexchange.com/questions/90089/rls-adaptive-filter-for-estimating-signal | <p>I am currently working on a project where i am to estimate a signal x_T using x_1 and x_2 with an RLS filter.</p>
<p>I have a problem where i don't quite get the results i am looking for. I think there is a problem with the filter coefficients. I don't know which ones i am to use.</p>
<p>This is what i have come up ... | 859 | |
adaptive filtering | autocorrelation of multiple signals | https://dsp.stackexchange.com/questions/73686/autocorrelation-of-multiple-signals | <p><strong>Problem:</strong> I am looking at an adaptive filtering application where the eigenvaluespread of the autocorrelation matrix <span class="math-container">$R$</span> is important for the convergence of the algorithm. For a <strong>single</strong> channel system the autocorrelation matrix <span class="math-con... | <p>You apply the same formula, but instead of using a scalar <span class="math-container">$x(n)$</span>, you will have <span class="math-container">$x(n) \in \mathbb{C}^{M \times 1}$</span>, where <span class="math-container">$M$</span> is the number of channels, and <span class="math-container">$x^{H}(n)$</span> is th... | 860 |
adaptive filtering | Adaptive Particle Filter: unknown process Equation | https://dsp.stackexchange.com/questions/81914/adaptive-particle-filter-unknown-process-equation | <p>In my design and implementation of a SIR particle Filter, I don't have the state process equation of the actual system, which would have given a very good estimation of the real signal. I was wondering, if there are any mathematical methods out there to extrapolate the next state (i.e construction of process equatio... | 861 | |
adaptive filtering | Approximate a Known System with Adaptive Filter and an Unknown System in a Series | https://dsp.stackexchange.com/questions/84700/approximate-a-known-system-with-adaptive-filter-and-an-unknown-system-in-a-serie | <p>I am using gradient descent on an adaptive IIR filter for the below system <a href="https://i.sstatic.net/Q6D6S.png" rel="nofollow noreferrer">1</a>. At the moment I am just assuming the known system is not there and it works fine. However, occasionally when the known system has slower dynamics it does not perform v... | <p>The problem with your diagram is that the calculation of the error isn't done on the output of the adaptive filter.<br />
The adaptive filter minimizes the error based on the idea the error is a function only of the weights of the filter and the input. In your cases it is also a function of the weights of the unknow... | 862 |
adaptive filtering | decision feedback equalizer building blocks (from Adaptive Filters: Theory and Applications” a book by Behrouz Farhang-Boroujeny) | https://dsp.stackexchange.com/questions/91920/decision-feedback-equalizer-building-blocks-from-adaptive-filters-theory-and-a | <p>Here you can see building blocks of DFE from <strong>"Adaptive Filters: Theory and Applications”</strong> a book by Behrouz Farhang-Boroujeny in chapter 17.</p>
<p>Figure 17.9 shows the overall building blocks of DFE which in the input we have noisy signal x that passed through channel and feeds to equalizer to... | 863 | |
adaptive filtering | Adaptive Filtering: Isn't the desired signal d(n) already known? | https://dsp.stackexchange.com/questions/94512/adaptive-filtering-isnt-the-desired-signal-dn-already-known | <p><a href="https://i.sstatic.net/bZHOLDIU.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bZHOLDIU.jpg" alt="LMS algorithm" /></a></p>
<p>When applying an algorithm like LMS, for example, in order to updates the weight coefficients I need the error signal at time <span class="math-container">$e[n]$</spa... | <p>The LMS algorithm uses <span class="math-container">$d[n]$</span> as a training signal to adapt the filter coefficients iteratively. This process is critical for training and tuning the filter to achieve the desired performance. Once trained, the filter can operate without requiring <span class="math-container">$d[n... | 864 |
adaptive filtering | LMS adaptive filter - is it Least mean square or least mean squares? | https://dsp.stackexchange.com/questions/83988/lms-adaptive-filter-is-it-least-mean-square-or-least-mean-squares | <p>It seems both names are used for the same algorithm:</p>
<p><strong>least mean square</strong> - mainly literature before 1990, for example: <em>Widrow, Bernard, and Samuel D. Stearns. "Adaptive signal processing prentice-hall." Englewood Cliffs, NJ (1985).</em></p>
<p><strong>least mean squares</strong> -... | <p>According <a href="https://www-isl.stanford.edu/%7Ewidrow/papers/j2005thinkingabout.pdf" rel="nofollow noreferrer">this</a> 2005 Stanford reference, "Thinking about Thinking, the Discovery of the LMS Algorithm", in 1960 the algorithm was baptized <em>least mean square</em>.</p>
<blockquote>
<p>I met Ted fo... | 865 |
adaptive filtering | Adaptive Digital Filter Block Diagram Question | https://dsp.stackexchange.com/questions/22325/adaptive-digital-filter-block-diagram-question | <p>I'm currently attempting to study up on adaptive digital filters. My book presents the diagram I've included below and I'm having trouble understanding conceptually what it's indicating. The problem deals with noise cancelation. The idea is that someone is driving and makes a phone call. The <em>x(k)</em> is their v... | <p>Judging from the figure, the situation is slightly different from your explanation in the question. The noise $v(k)$ is the actual noise in the signal, not the noise picked up by the reference microphone. So the noisy signal is $d(k)=x(k)+v(k)$. If you knew $v(k)$ you could simply subtract it from $x(k)$ without the... | 866 |
adaptive filtering | Why are Some Filter implementations Preferable for Adaptive IIRS? | https://dsp.stackexchange.com/questions/85359/why-are-some-filter-implementations-preferable-for-adaptive-iirs | <p>I am aware that some filter implementations such as <a href="http://www.signal.uu.se/Staff/pd/DSP/Doc/applicat/chap6.pdf" rel="nofollow noreferrer">lattice/ladder</a> and <a href="https://www.dsprelated.com/freebooks/filters/Series_Parallel_Filter_Sections.html" rel="nofollow noreferrer">SoS sections</a> are advanta... | <p>I don't know why lattices converges faster.
But I know why cascades are hard to converge. Assume you want only a delayed impulse as impulse response. you have many options to achieve this intuitively. This will impose it to slower convergense and multimodality. Im also waiting for others to provide more comprehensiv... | 867 |
adaptive filtering | Adaptive Band pass filter for extracting respiratory waveform from accelerometer data | https://dsp.stackexchange.com/questions/59831/adaptive-band-pass-filter-for-extracting-respiratory-waveform-from-accelerometer | <p>I am recording data from an accelerometer attached to the chest (1000Hz). I need to extract the respiratory waveform. I tried an adaptive bandpass filter based on a dominant frequency in my signal based on <a href="https://cutt.ly/j24zdj" rel="nofollow noreferrer">https://cutt.ly/j24zdj</a>.</p>
<p>Steps in brief: ... | <p>Under the extremely controlled conditions required to measure respiratory rate using this method, you can try to use the <a href="https://en.wikipedia.org/wiki/Autocorrelation" rel="nofollow noreferrer">autocorrelation</a> (which is more robust in the presence of noise) to determine the "dominant" frequency in your ... | 868 |
adaptive filtering | sampling frequency of GPS | https://dsp.stackexchange.com/questions/25111/sampling-frequency-of-gps | <p>Now I am trying to design FIR based adaptive filter for rejection of Jamming in GPS device. (just self-learning purpose, Jamming is simple tone)</p>
<p>I've designed NOT-BAD performance adaptive filter for low sampling frequency. (~44100 Hz)</p>
<p>But when I use this adaptive filter for high sampling frequency (1... | <p>C/A code (the main civilian channel as of now) has a main lobe of around 2MHz and depending on how much processing you want to do, it is normally sampled in the low MHz range, which you are in. (you could pull it off with 2-5MHz).</p>
<p>Do know that the signal must be mixed down to a lower frequency before you sam... | 869 |
adaptive filtering | Difference between 'conventional' and 'adaptive' beamformers? | https://dsp.stackexchange.com/questions/7825/difference-between-conventional-and-adaptive-beamformers | <p>This <em>might</em> be a terminology question but I am not sure. </p>
<p>Basically, what is the difference between <em>conventional</em> beamformers, and <em>adaptive</em> beamformers? I thought that all beamformers were inherently adaptive to some criteria, like minimization of distortion or variance, or some othe... | <p>A beamformer is basically a spatial filter. It can be passive, just like a temporal filter. </p>
<p>Instead of samples separated by time, they are separated by space. A passive temporal filter can be a bandpass that is "aimed" or "steered" at a particular frequency. For passive spatial filters (i.e. beamformers... | 870 |
adaptive filtering | Adaptive LMS Algorithm MATLAB | https://dsp.stackexchange.com/questions/53461/adaptive-lms-algorithm-matlab | <p>I'm having some trouble implementing my LMS Adaptive Filter in MATLAB to separate wideband and narrowband signals from a voice signal.</p>
<p>I'm using a delayed version of my input as a reference as well as the error term.</p>
<pre><code>step = 0.01;
w = zeros(1, N);
xDelayed = [zeros(1, 100) x']'; % delaying in... | <p>There are several problems in your code. First, it looks like you're confusing iteration and vector indices. The computation of <code>e</code> should use <em>all</em> values of the current (delayed) data vector, filtered with the current filter coefficients. In the update equation, you subtract a scalar from a vecto... | 871 |
adaptive filtering | Why does diagonal loading of a covariance matrix make an adaptive beamformer more robust in the case of a perturbed array? | https://dsp.stackexchange.com/questions/303/why-does-diagonal-loading-of-a-covariance-matrix-make-an-adaptive-beamformer-mor | <p><a href="https://dsp.stackexchange.com/questions/146/how-can-one-improve-the-robustness-of-adaptive-beamformers-to-signal-mismatches">It has been shown</a> that 'diagonal loading' a covariance matrix derived for an adaptive beamformer can improve robustness of the beamformer when the antenna array is perturbed, albe... | <p>I had worked on an array processing problem where I had used diagonal loading of the measurement covariance matrix. But I had used diagonal loading as a solution to what I thought was a numerical issue with my eigen values being too small. Since I had to invert the covariance matrix with small eigen values, I had nu... | 872 |
adaptive filtering | Adaptive equalizer for IIR channel? | https://dsp.stackexchange.com/questions/17838/adaptive-equalizer-for-iir-channel | <p>I am quite new to the idea of equalization. I have a few queries regarding the same.</p>
<ul>
<li>In my application I require to equalize a channel whose impulse response is an IIR response. Is it possible to design an adaptive equalizer based on LMS algorithm to equalize it? I tried some MATLAB simulations and it ... | <p>Note that the inverse of an FIR system is IIR, and the same is true for the inverse of an IIR system, unless it is an all-pole system, the inverse of which would be FIR. So in most cases the ideal equalizer should have an infinitely long impulse response in order to perfectly invert the channel. In practice almost a... | 873 |
adaptive filtering | Filter processing - frequency to time, truncate taps, and back to frequency domain (using Python) | https://dsp.stackexchange.com/questions/95783/filter-processing-frequency-to-time-truncate-taps-and-back-to-frequency-doma | <p>I read a paper about adaptive filtering specifying the following procedure:
<span class="math-container">$$ q_{FIR}(k) \overset{\textrm{FIR}}{\longleftarrow} q(k)$$</span></p>
<p>The framework processes the input signal (sampled in <span class="math-container">$f_s$</span> sampling rate) using STFT and works batch b... | 874 | |
adaptive filtering | Adaptive equalization vs inverse of transfer function | https://dsp.stackexchange.com/questions/63914/adaptive-equalization-vs-inverse-of-transfer-function | <p>I have the following equalization problem as shown in the figure below:</p>
<p><a href="https://i.sstatic.net/O9Ws2.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/O9Ws2.png" alt=""></a></p>
<p>Now I can compute the coefficients for my adaptive FIR filter c (dim(c) = N) the following:<br>
<span clas... | <p>Inverting a channel can only be done when the channel is a minimum phase system (trailing echos only). A minimum phase system is characterized as having all zeros in the left half plane (for the s plane, or equivalently in a sampled system and the z plane all zeros inside the unit circle). Inverting such a channel r... | 875 |
adaptive filtering | Least Mean Squares Algorithm confusion with Adaptive Line Enhancement | https://dsp.stackexchange.com/questions/53444/least-mean-squares-algorithm-confusion-with-adaptive-line-enhancement | <p>I'm just a bit confused about the least mean squares algorithm to separate wideband and narrowband in an adaptive filter for voice conversation. I'm interested in the narrowband part and I'm confused about the LMS equation as follows:</p>
<p><a href="https://i.sstatic.net/ghBem.png" rel="nofollow noreferrer"><img s... | <p>I recommend you read up on the <a href="https://en.wikipedia.org/wiki/Least_mean_squares_filter" rel="nofollow noreferrer">LMS algorithm</a> and try to understand it before you start implementing it, otherwise you won't be able to find any errors in your code. In that formula, the index <span class="math-container">... | 876 |
adaptive filtering | Adaptive Wiener Filter Coefficients Calculation | https://dsp.stackexchange.com/questions/11422/adaptive-wiener-filter-coefficients-calculation | <p>I want to extrapolate a signal <strong>X</strong> of length 11, using the weiner filter coefficients <strong><em>W</em></strong> of length 7. The procedure I am using is as follows:</p>
<ol>
<li>Compute the autocorrelation matrix upto lag 8 .</li>
<li>Using Levinson recursion, invert the autocorrelation matrix <str... | <p>The Wiener filter is, by definition </p>
<p>a) not adaptive and </p>
<p>b) not FIR / AR. </p>
<p>You seem to want an adaptive FIR filter. </p>
<p>There are many variants of this: <a href="http://en.wikipedia.org/wiki/Least_mean_squares_filter" rel="nofollow">LMS</a>, <a href="http://en.wikipedia.org/wiki/Least_m... | 877 |
adaptive filtering | Echo cancellation supporting long delays and without frequency domain processing | https://dsp.stackexchange.com/questions/26689/echo-cancellation-supporting-long-delays-and-without-frequency-domain-processing | <p>AEC algorithms mostly rely on LMS adaptive filtering, i.e. you update FIR filter coefficients then perform the filtering. Theoretically, the FIR must be as long as the maximum echo length you want to cancel. For instance to cancel delays up to 500ms on a 48kHz signal, you'll need a 24000 point FIR.
When your memory ... | <p>I believe you logic is reasonable. The fact that there are companies offering algorithms for long echo tail (even above 1 second) with reasonable performance indicates that an algorithm similar to your suggested logic can work.</p>
| 878 |
adaptive filtering | How to Remove Gaussian Noise from an Image without Destroying the Edges? | https://dsp.stackexchange.com/questions/1365/how-to-remove-gaussian-noise-from-an-image-without-destroying-the-edges | <p>What is the best filter for removing Gaussian noise without destroying the edges? I am using the standard Lena images with additive Gaussian noise and I want to denoise before applying anisotropic diffusion. I don't want to median filter because edges become blurred. I tried adaptive filtering but results were not s... | <p>You might need to consider more advanced techniques. Here are two recent papers on edge-preserving denoising:</p>
<ul>
<li><p><a href="http://dx.doi.org/10.1109/TIP.2006.877409">Edge-Preserving Image Denoising via Optimal Color Space Projection</a> <a href="http://web.mysites.ntu.edu.sg/zvitali/publications/.../col... | 879 |
adaptive filtering | Need a fast algorithm of adaptive convolution | https://dsp.stackexchange.com/questions/10561/need-a-fast-algorithm-of-adaptive-convolution | <p>I have to apply some kind of adaptive filter to my function $f(x).$ I present each point of my signal as a Gaussian, whose bandwidth depends on its location <strong>(not the point of observation $\textbf{x}$)</strong> as $h(t),$ which is a known pre-calculated function. The final output function $s(x)$ is a superpos... | 880 | |
adaptive filtering | When is Normalized LMS better than LMS? | https://dsp.stackexchange.com/questions/83564/when-is-normalized-lms-better-than-lms | <p>I see mention that normalized LMS "usually converges faster than LMS", in Diniz "Adaptive Filtering" p.152, can this be made more precise? IE, for which signal distributions does it hold?</p>
<p>I'm in particular interested in overparameterized regime where misadjustment is zero for LMS and NLMS.... | 881 | |
adaptive filtering | What is the difference between the Weiner-Hopf equation and the normal equation? | https://dsp.stackexchange.com/questions/17632/what-is-the-difference-between-the-weiner-hopf-equation-and-the-normal-equation | <p>In adaptive filters, the development of LMS algorithm typically starts from the Weiner-Hopf equation, while the development of RLS algorithm starts from the normal equation. As I understand, these two equations are the same, and both their solutions is the optimal coefficients that the adaptive filter has to find. ... | <p>Weiner-Hopf equation leads to Wiener filter that is optimal filter. For the case of stationarity in some time span it's the only filter minimizing MSE at its output. LMS and RLS algorithms are the adaptive approaches and they converge to Wiener optimal solution (as you can see from their convegence curves). While LM... | 882 |
adaptive filtering | How is it determined that an adaptive filter has converged? | https://dsp.stackexchange.com/questions/28366/how-is-it-determined-that-an-adaptive-filter-has-converged | <p>Is it when the cost function such as the error signal or Mean Square Error (MSE) signal is minimised?</p>
| <p>The adaptive filter is converged when the error is what they call Wide Sense Stationary, meaning the mean and variance of the error are unchanging over long time intervals.</p>
| 883 |
adaptive filtering | Why is the error between the desired signal and estimated signal in the case of LMS filter remaining constant even after n number of iterations | https://dsp.stackexchange.com/questions/64515/why-is-the-error-between-the-desired-signal-and-estimated-signal-in-the-case-of | <p><a href="https://i.sstatic.net/huadl.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/huadl.jpg" alt="enter image description here"></a><a href="https://i.sstatic.net/p7Tm1.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/p7Tm1.jpg" alt="Image shows the matlab code of lms algorithm."></a>... | <p>As mentioned in the comment, I modified the code given here and was able to adapt the LMS filter with error tapering to zero. The only assumption I made is that (since I am not an audio expert and do not know how the channel from speaker to the microphone would look like), I assumed a 10 tap channel with only first ... | 884 |
adaptive filtering | Noise cancellation using RLS filter | https://dsp.stackexchange.com/questions/43075/noise-cancellation-using-rls-filter | <p>I am trying to create an adaptive noise canceller using the RLS algorithm. The dsp toolbox from matlab offers <a href="https://de.mathworks.com/help/dsp/ref/dsp.rlsfilter-class.html" rel="nofollow noreferrer">the RLS adaptive filter</a> already implemented, so this saved me some trouble.</p>
<p>My goal is to filter... | 885 | |
adaptive filtering | How do state of the art echo cancellation algorithms deal with variable propagation times of sound due to multiple speakers or reverberation? | https://dsp.stackexchange.com/questions/50679/how-do-state-of-the-art-echo-cancellation-algorithms-deal-with-variable-propagat | <p>I understand how echo cancellation works with a single speaker and no reverberation (using adaptive filtering and freezing the coefficients during double-talk). However, in cases with more than one speaker source or reverberation causing different propagation of the same signal, would this not completely change the ... | 886 | |
adaptive filtering | How the Gain Term $ K \left( n \right) $ Is Derived? Why Is It Called Gain? | https://dsp.stackexchange.com/questions/35337/how-the-gain-term-k-left-n-right-is-derived-why-is-it-called-gain | <p>In "adaptive filter theory" and "advance signal processing and Noise reduction" they have directly come up with the term gain without stating how they got it.</p>
<p>In adaptive filter theory they have jumped from equation 13.16 to 13.18.</p>
<p><a href="https://i.sstatic.net/Ene7I.png" rel="nofollow noreferrer"><... | <p>In all adaptive signal processing schemes, be it a Least Mean Squares (LMS), Recursive Least Squares (RLS) or a Kalman Filter, The fundamental concept is the <strong>update</strong> of some parameter: such as the vector filter coefficients of a Transversal Tapped Delay Line (an FIR indeed) structure of LMS or a stat... | 887 |
adaptive filtering | Difference between Leaking Factor and Forgetting Factor | https://dsp.stackexchange.com/questions/42938/difference-between-leaking-factor-and-forgetting-factor | <p>I am using a Recursive least square adaptive filter to process electromyography signals and it is working decently so far. I decided to implement an LMS adaptive filter as a noise cancellation, so that I can compare the results, however, going through the matlab documentation for the <a href="https://de.mathworks.co... | <p>The play similar role in those algorithms - the ability to forget the past and adapt to current reality. </p>
<p>In the LMS, the classic implementation has $ \alpha = 1 $.<br>
Namely the optimal weights at any point are function of all inputs. </p>
<p>The Leakage factor allows to weigh the past differently in a ... | 888 |
adaptive filtering | Non-linear signal mean? | https://dsp.stackexchange.com/questions/97847/non-linear-signal-mean | <p>While reading a book on adaptive filter, I have came across a term 'nonlinear' associated with signal.</p>
<p>But I have learned about the linear and non linear system, which is defined by the principle of homogeneity and additive. I am curious to know the definitions of a non-linear signal. I have search over the i... | <blockquote>
<p>I am curious to know the definitions of a non-linear signal</p>
</blockquote>
<p>There is no such thing. Linearity (or lack thereof) are a property of systems, not signals. Linearity is only defined for the relationship between an input and an output signal. The term and it's definition are meaningless... | 889 |
adaptive filtering | what is the difference between LMS and MPC? | https://dsp.stackexchange.com/questions/73701/what-is-the-difference-between-lms-and-mpc | <p>I do understand that MPC is a control method and requires known model in the feedback path.
LMS, on the other hand, is more like an adaptive filtering, which estimates the tap coefficients yielding the minimum mean squared error. Plus, LMS does not require known model.</p>
<p>Besides the differences I mentioned abov... | 890 | |
adaptive filtering | Modeling ADC in Active Noise Cancellation | https://dsp.stackexchange.com/questions/28058/modeling-adc-in-active-noise-cancellation | <p>I'm tinkering in Matlab with a problem that's very similar to active noise cancellation. In the literature, the secondary path is described as the transfer function from the output of the adaptive filter to the error input sensor. The algorithm needs to model this path to obtain good results.</p>
<p>However, ther... | <p>You are correct that the system will attempt to invert the ADC filter. In acoustics this is not usually a problem because there is not much energy at those frequencies.
If your application is not a standard acoustic system, there may be an opportunity to put a copy of the ADC filter in the plant path (this is norma... | 891 |
adaptive filtering | How to design a filter that can filter out noise accurately, after setting the parameters of the filter using standard signal? | https://dsp.stackexchange.com/questions/67728/how-to-design-a-filter-that-can-filter-out-noise-accurately-after-setting-the-p | <p>I meet a problem with designing a filter. I have two different instruments that could measure the same AC signal (usually ~200hz, always <1kHz), <strong><em>A</em></strong> and <strong><em>B</em></strong>. <strong>A</strong> can carry out signal measurement during the normal operation of the instrument.
<strong>... | <p>If you can use a higher precision instrument to measure the signal, then, if the signal maintains it's characteristics, you can build a system's model and use a Kalman filter for the "not so good" input channel.</p>
| 892 |
adaptive filtering | Removing low frequencies from a signal | https://dsp.stackexchange.com/questions/43374/removing-low-frequencies-from-a-signal | <p>I am trying to remove low frequencies from a signal and intuitively I chose the high-pass filter, more specifically - a Butterworth filter, Order 4 (because I am not sure how to choose properly the order and 4 seemed as a good choice) and cutoff frequency of 50 Hz. The problem is, that the filter removes the low fre... | <p>You want to remove the heart beat signal and keep the "noise". We can solve this problem by using a denoising algorithm, and subtracting the denoised signal from the original signal.</p>
<p>Setting frequency cutoffs for a frequency domain filter can get tricky and turn into a game of whack-a-mole because there's "h... | 893 |
adaptive filtering | Adaptive calculations of Wiener filter coefficients | https://dsp.stackexchange.com/questions/11475/adaptive-calculations-of-wiener-filter-coefficients | <p>Suppose,I have an input of length of lenght 100. data=[x0...x99];
I take a window of lenght 11 from x0 to x10.
windowed data=[x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10],
now, I compute 7 wiener coefficients which are
[w0 w1 w2 w3 w4 w5 w6];
next I will move by window one sample forward,
new windowed data= [x1 x2 x3 x4 x5... | 894 | |
adaptive filtering | What is an Adaptive Mean Filter? | https://dsp.stackexchange.com/questions/29513/what-is-an-adaptive-mean-filter | <p>$$\hat f(x, y) = g(x, y)-\frac{\sigma_n^2}{\sigma_L^2}\left[g(x, y)-m_L\right]$$</p>
<p>What are the meanings of the following terms:</p>
<ul>
<li>$m_L$</li>
<li>${\sigma_\eta}^2$</li>
<li>${\sigma_L}^2$</li>
</ul>
<p>Here we see that $m_L$ is subtracted from the Image and then the whole term is multiplied by $\f... | <p>A wild guess. $L$ denotes a region $R$ around pixel $g(x,y)$, potentially a symmetric one of size $(2L+1)\times (2L+1)$. $m_L$ and $\sigma_L^2$ are the average and variance in $R$. And $\sigma_n^2$? Probably the estimated noise variance over the whole image, supposed stationary.</p>
<p>In a flat region with noise ... | 895 |
adaptive filtering | AEC Speex . How does it work? | https://dsp.stackexchange.com/questions/15075/aec-speex-how-does-it-work | <p>I'm working with AEC of Speex. The algorithm is based on the MDF adaptive filter + an adaptive learning rate. I'm using it like a ANC and it works very well.
Does anybody have some material, as block scheme, data flow diagram of the AEC of Speex.
I have read the documentation but it is not very useful for the dsp co... | 896 | |
adaptive filtering | What is causing my ANC LMS update to diverge? | https://dsp.stackexchange.com/questions/73668/what-is-causing-my-anc-lms-update-to-diverge | <p>I'm trying to implement a simulation of an ANC system with python, using this model <a href="https://www.mathworks.com/help/audio/ug/active-noise-control-with-simulink.html#d122e12289" rel="nofollow noreferrer">here</a>. <a href="https://i.sstatic.net/5sCIt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.... | <p>Turns out it's just a scaling issue. Because the struck.unpack() gives out a signed 16-bit value, the step size is too large for it. Two ways to go around this, you scale down your input and scale back up when outputting, or you just adjust the step size mu.</p>
<p>I used a mu value of 10e-8 and seems like this valu... | 897 |
adaptive filtering | What's the Difference Between LMS and Gradient Descent Adaptation? | https://dsp.stackexchange.com/questions/30605/whats-the-difference-between-lms-and-gradient-descent-adaptation | <p>I found algorithms that seems the same to me, but they are described with different names (in field of adaptive filtering).</p>
<p>For example:</p>
<ol>
<li><p><strong>LMS - least-mean-squares</strong> seems to be <strong>GD - stochastic gradient descent</strong> </p></li>
<li><p>Often the <strong>stochastic gradi... | <p>The LMS algorithm is based on the idea of gradient descent to search for the optimal (minimum error) condition, with a cost function equal to the mean squared error at the filter output. However, it doesn't actually calculate the gradient directly, as that would require knowing:</p>
<p>$$
E(\mathbf{x}[n]e^*[n])
$$<... | 898 |
adaptive filtering | NLMS algorithm for a MISO structure | https://dsp.stackexchange.com/questions/55874/nlms-algorithm-for-a-miso-structure | <p>I am trying to implement an NLMS algorithm for a multi-input single-output(MISO) structure. </p>
<p>We take a reference signal x, then we made a new set of P input signals from it as follows: x_op (k) = x(k)^p. k denotes the k-th sample of our reference signal x.</p>
<p>For the case where P = 1, our adaptive filte... | <p>I can provide you coding example, but it solves more generic problem than you posted. It is for general dynamic system that converts two inputs x(t), y(t) into single output z(t) and defined by Urysohn integral equation. Hammerstein is particular case of Urysohn and linear system is particular case of Hammerstein. T... | 899 |
filter design | Abs(poles) < 1 by what margin for a stable filter? | https://dsp.stackexchange.com/questions/3057/abspoles-1-by-what-margin-for-a-stable-filter | <p>I checked the literature for recent algorithms used to design a digital filter that is a minimax approximation of a desired frequency response. All the articles I found work out examples where all the poles have magnitude less than 0.92, or less that 0.89, etc. I havn't seen a published example with a pole having ma... | <p>It would most likely depend upon the order of the filter, but having a pole at position $z_p$ where $|z_p| = 0.95$ shouldn't pose a stability problem if you're using double-precision floating-point arithmetic with a filter of reasonable length.</p>
<p>Since I don't know anything about your specific application, one... | 900 |
filter design | Bessel filter second-order sections Q and Fc multiplier derivation | https://dsp.stackexchange.com/questions/7830/bessel-filter-second-order-sections-q-and-fc-multiplier-derivation | <p><a href="http://freeverb3.sourceforge.net/iir_filter.shtml" rel="nofollow">A practical guide for digital IIR audio filters</a> has cookbook-style values for creating higher-order Bessel filters out of biquads, but the values listed aren't very precise:</p>
<pre><code>You should multiply the Fc for each stage by the... | <p>There is no simple closed-form equation to calculate Bessel filter bi-quad coefficients. The poles of the filter come from a Bessel polynomial. Higher order Bessel polynomials are determined using a recursion relationship. You need computer algorithms to calculate the poles and resolve the bi-quad coefficients. </p>... | 901 |
filter design | Choice of cost function in adaptive noise cancellation | https://dsp.stackexchange.com/questions/8165/choice-of-cost-function-in-adaptive-noise-cancellation | <p>Why is the least squares cost function used in adaptive noise cancellation with the recursive least squares (RLS) algorithm, but the mean squared error used in signal estimation? </p>
<p>For an ergodic source (where time and ensemble averages should be the same) I would have thought the choice was arbitrary.</p>
<... | <p>You are actually asking 2 separate questions. If I have interpreted your post correctly, they are:</p>
<ol>
<li>Why is the RLS used in Noise Cancellation, whereas the LMS is used in signal estimation?</li>
<li>(If we assume that the signal is ergodic) Isn't minimising the Ensemble average, $E\{e_n^2 \}$, equivalent... | 902 |
filter design | How does a FIR equiripple filter behave close to DC? | https://dsp.stackexchange.com/questions/10460/how-does-a-fir-equiripple-filter-behave-close-to-dc | <p>I am multiplying two sine waves with the same frequency (f), but might have a phase difference 0 <-> 90 degrees. The product is a two frequency sinusoidal wave with f1 = f-f = DC and f2 = f+f = 2f. I now want to filter out the 2f component. I am currently sampling at Fs = 32 x f. I get a 40th order equiripple FIR... | <p>You're correct; if the signal that you're applying to the input of the filter isn't exactly at DC (0 Hz), then you might see a slight difference in the amplitude of the output due to the filter's passband ripple. I would assert that for most applications, this is either imperceptible or negligible for typical values... | 903 |
filter design | fir filter - mean delay and snr from difference equation? | https://dsp.stackexchange.com/questions/15048/fir-filter-mean-delay-and-snr-from-difference-equation | <p>I'm trying to get my dsp sea legs a bit, and am trying to complete a problem that asks for the mean delay and expected SNR boost for a given difference equation: y[n] = (x[n] + ... + x[n-N+1])/N</p>
<p>I'd love some general guidance on how to learn more about how to address this. Specifically,</p>
<ul>
<li>I'd lik... | <p>I'll give you some hints to help you solve the problem by yourself. Looking at the input-output relation, you can see that the output signal is computed only from a combination of delayed input signal values, and not from delayed output signal values. So your impulse response has a finite length and the filter can b... | 904 |
filter design | Why are recursives methods useful for FIR filter design? | https://dsp.stackexchange.com/questions/17198/why-are-recursives-methods-useful-for-fir-filter-design | <p>As I understand it, FIR filtering is a linear process. That mean for me that the whole filtering process will have a fully predictable behavior.
So, could someone explain why a universal deterministic and optimal filter design method to obtain the desired response doesn't exist and why recursive approach seems to ... | <p>Sure, FIR filters are "simple" linear objects. But a typical FIR filter design task looks like this:</p>
<blockquote>
<p>Find a set of numbers (the filter coefficients) such that the
magnitude of their Discrete Fourier Transform is as close as possible to a
target response. "As close as possible" being define... | 905 |
filter design | Which values do I use to filter a specific frequency with an RLC circuit? | https://dsp.stackexchange.com/questions/18829/which-values-do-i-use-to-filter-a-specific-frequency-with-an-rlc-circuit | <p>I have a RLC circuit with transformation $$H(s) = \frac{R}{Ls+\frac{1}{Cs}+R}$$ and I know that by setting $s=j\omega$ I can obtain the frequency response of this system. What I don't understand is how I can use the frequency response graph to decide which values I should set on R and f $(L=2\pi f, C=1\mu F)$ to fil... | 906 | |
filter design | Why this two FIR filters have the same amplitude but different phase response | https://dsp.stackexchange.com/questions/22728/why-this-two-fir-filters-have-the-same-amplitude-but-different-phase-response | <p>Why a filter of the form </p>
<p>$$
1+a_0 z^{-1} +a_1 z^{-2}+ a_2 z^{-3}
$$
has the same amplitude response when in the reversed form
$$
a_2+a_1 z^{-1} +a_0 z^{-2}+z^{-3}
$$
but the phase response is different. I don't get it, and can't understand what the differences in terms of the relative group delays mean.</p>... | <p>If you have a causal length $N$ FIR filter with impulse response $h[n]$, and with frequency response $H(e^{j\omega})$, and you invert it on the time axis, you get a new filter</p>
<p>$$g[n]=h[-n]\tag{1}$$</p>
<p>This filter is non-causal, but since it is an FIR filter, it can be made causal by shifting it to the l... | 907 |
filter design | Any simple Digital All-Pass Filter Design Tools? | https://dsp.stackexchange.com/questions/24031/any-simple-digital-all-pass-filter-design-tools | <p>I would like to be able to implement an All-Pass filter with a frequency-dependent group delay. I need a maximum group delay at low frequency of about 20 samples (for F<em>s</em> = 44.1kHz), and it needs to fall to zero(-ish) at the Nyquist frequency. Ideally, I would like to specify a corner frequency and a rate ... | <p>This is an excerpt from the FilterScript user's guide, which should provide you with enough information on how to design the filter. Please refer to the other product resources on <a href="http://www.advsolned.com/asn_filter_designer.html" rel="nofollow noreferrer">the tool's homepage for more information.</a></p>
... | 908 |
filter design | Is it possible to design a digital filter that rejects 60Hz noise while keeping step response in the time domain below one mili-second | https://dsp.stackexchange.com/questions/26161/is-it-possible-to-design-a-digital-filter-that-rejects-60hz-noise-while-keeping | <p>Have been trying to design IIR and FIR 60Hz notch filters but all have step response way above 10ms. </p>
| <p>You can trade off steepness of the notch against time domain ringing. That's a fundamental trade off and there is no way around it. When using an IIR notch you can simply adjust the "Q" (quality factor). A Q of 3 will give a step response that's roughly 10ms long. </p>
| 909 |
filter design | How to find out the farrow coefficients if FIR coefficients are given? | https://dsp.stackexchange.com/questions/27094/how-to-find-out-the-farrow-coefficients-if-fir-coefficients-are-given | <p>FIR filter coefficients are known. Then what is the matlab code or function that is used to determine the corresponding farrow structure coefficients? </p>
| <p>There is no standard way to determine the coefficients of the Farrow structure for a given FIR filter. The Farrow structure is an implementation of a whole class of FIR filters with transfer function(s) $H_{\mu}(z)$ with a continuous control parameter $\mu$. Often this parameter $\mu$ determines a fractional delay, ... | 910 |
filter design | Max useful filter tap count for given fixed point bitwidth | https://dsp.stackexchange.com/questions/37314/max-useful-filter-tap-count-for-given-fixed-point-bitwidth | <p>I have a 10 bit ADC sample stream in which I would like to apply a digital band pass filter. Is there a theoretical filter tap count that would define the threshold of "usefulness"? </p>
<p>I guess my thought process is: There are only 10 bits, so at some point (via increasing the tap count) the attenuation will be... | <p>Since you can widen your bit width with each operation, no, there's no such maximum useful width.</p>
<p>Take GPS receivers as an example: many of them <sup>citation needed</sup> use 2 bit ADCs and yet are useful, because the signal, already hidden in noise before it reaches the ADC, only gets "visible" by massive ... | 911 |
filter design | what is the suitable design Method to the filter? | https://dsp.stackexchange.com/questions/38620/what-is-the-suitable-design-method-to-the-filter | <p>hi i'm going to design a low pass FIR filter for an EEG signal for the detection of eppileptic siezure and i want to know what is the suitable design Method to the filter? i need this FIR filter just to smooth the signal to use it for discret wavelet transform.
thanks</p>
| <p>For a quick filter design without getting into trouble, I recommend avoiding any IIR structure and design an FIR using either least squares (firls in matlab) or Parks McClellan (firpm in matlab, remez in octave). There are plenty of answers here on how many taps you will need, (such as <a href="https://dsp.stackexch... | 912 |
filter design | Why low-pass FIR Equiripple filter is designed with 3 dB of ripple in the pass-band and at least 60 dB of attenuation in the stop-band? | https://dsp.stackexchange.com/questions/38759/why-low-pass-fir-equiripple-filter-is-designed-with-3-db-of-ripple-in-the-pass-b | <p>Please tell me, why low-pass FIR Equiripple filters are designed with 3 dB of ripple in the pass-band and at least 60 dB of attenuation in the stop-band
and not other values ?
I want to know are these values simply a convention?</p>
| <p>Stop band attenuation is a good thing right? After all it's the primary reason why you want a frequency selective filter: stop the unwanted frequencies. So a 60dB attenuation in the stop band of a filter is considered to be the norm in many typical applications. But not always so, as the comments indicate; you must ... | 913 |
filter design | Direct form I and Direct form II | https://dsp.stackexchange.com/questions/46046/direct-form-i-and-direct-form-ii | <p>I was studying about realization structures of digital filters. Is it mandatory to have the order of numerator must be less than that of denominator of transfer function for realization of filter using direct form I and II?</p>
| <p>no. but, for a <strong>causal</strong> LTI digital filter with a rational transfer function, it is necessary that the number of zeros, $M$, not exceed the number of poles, $N$.</p>
<p>$$\begin{align}
\\
H(z) \triangleq \frac{Y(z)}{X(z)} & = H_0 \frac{(z-q_1)(z-q_2)(z-q_3)...(z-q_M)}{(z-p_1)(z-p_2)(z-p_3)...(z... | 914 |
filter design | What is meant by "arbitrary" in the context of digital filter design? | https://dsp.stackexchange.com/questions/51111/what-is-meant-by-arbitrary-in-the-context-of-digital-filter-design | <p>I try to understand the 'arbitrary' what does it meant?
I had read many references ,such a one it is 'begin the process with a transfer function of your choice' ,in other reference :related by the starting point,</p>
<p>In other hand i read about Chebyshev approximation with arbitrary magnitude,
how can i find the ... | <p>The term "arbitrary" in this context refers to the desired frequency response, and what it means is that the respective design method accepts any desired response. So unlike required by many standard design routines, the magnitude response does not need to be piecewise constant or linear, and, more importantly, the... | 915 |
filter design | FIR filter window method | https://dsp.stackexchange.com/questions/56586/fir-filter-window-method | <p>In the window method for filter design it is explained that we do an ideal filter and then we pass it to time domain, but it will be time limited and then...</p>
<p>Why don't we filter directly in the frequency domain?</p>
| 916 | |
filter design | Ripples in filter | https://dsp.stackexchange.com/questions/60113/ripples-in-filter | <p>What are the uses of ripples in the filter design. We try to design a filter with least ripples but sometimes we design a filter to have 2 or 3 ripples. Why is it so? </p>
| <p>Ripples are usually an undesired side effect. E.g., when designing a frequency selective filter you normally want a piecewise constant magnitude of the frequency response, but this is physically impossible.</p>
<p>Certain design criteria result in filters without ripples, such as the Butterworth criterion, which re... | 917 |
filter design | Analytic solution for non-flat filter design | https://dsp.stackexchange.com/questions/64858/analytic-solution-for-non-flat-filter-design | <p>I'm trying to write an accelerometer calibration script that uses filters to convert from volts into <span class="math-container">$m/s^2$</span>. As accelerometers tend to have non-flat response curves, this means I have to design a rather complex filter. I'm not worried about phase, as I can just apply the filter... | <p>If you are not concerned on the phase and just want to approximate a magnitude response, then your first option should be the <strong>frequency sampling</strong> method implemented in Matlab/Octave fir2() function.</p>
<p>You would provide the frequency grid and corresponding frequency response magnitude at those f... | 918 |
filter design | invfreqz() and frequency domain filter specification | https://dsp.stackexchange.com/questions/68166/invfreqz-and-frequency-domain-filter-specification | <p>I am trying to go from a time-domain description of a filter, via frequency domain, generating a filter based on that frequency domain description, then seeing how far from the original I end up.</p>
<pre><code>L = 10-1;
h = zeros(L+1,1);
h(2) = 1;
L2 = 1024-1;
H = fft(h, L2+1);
H1 = H(1:(L2/2+2));
W = 2*pi*(0:(L2+... | <p>The warning is due to modeling a unit delay which has wide (constant) frequency response thus will have very large number differences (ill conditioned matrices) in the translation between domains and looking for an IIR solution to the FIR problem (note that the algorithm converges to a trivial but valid solution whe... | 919 |
filter design | Formula for designing Lynn's low pass filter | https://dsp.stackexchange.com/questions/73983/formula-for-designing-lynns-low-pass-filter | <p>For the second order Lynn's low pass filter, the general form of the transfer function is:
<span class="math-container">$$
H(z)=\frac{(1−z^{-m})^2}{ (1−z^{-1})^2 }
$$</span>
where <span class="math-container">$m$</span> is a positive integer. The gain for this is <span class="math-container">$m^2$</span>, time delay... | <p>Meanwhile, we have got an approximation solution for this. Consider the equation:
<span class="math-container">$$
\frac{1}{\sqrt2}=\frac{\sin^2(m\pi f_c /f_s)}{m^2\sin^2(\pi f_c /f_s)}
$$</span></p>
<p>In the right-hand side denominator, since <span class="math-container">$f_c << f_s$</span>, we can write: <sp... | 920 |
filter design | Where to learn about "analog prototype filters"? | https://dsp.stackexchange.com/questions/51277/where-to-learn-about-analog-prototype-filters | <p>Where to learn about "analog prototype filters"?</p>
<p>I've heard about them, but I'm unsure about what they really are and how they're constructed.</p>
| <p>"Analog prototype" filters are well-known analog filters that have specific desirable properties. They include (but aren't limited to):</p>
<ul>
<li><a href="https://en.wikipedia.org/wiki/Butterworth_filter" rel="nofollow noreferrer">Butterworth filters</a>: maximally-flat passband response</li>
<li><a href="https:... | 921 |
filter design | What is the construction of this filter | https://dsp.stackexchange.com/questions/75884/what-is-the-construction-of-this-filter | <p>I have built a resonance filter using the code from <a href="https://wiki.multimedia.cx/index.php/Impulse_Tracker#IT214_sample_compression" rel="nofollow noreferrer">here</a> I would like to know what the construction of this filter is. I believe it is an IIR and that it is probably a second order/two pole filter bu... | <p>This beginning of this answer is a reformatting of <a href="https://wiki.multimedia.cx/index.php/Impulse_Tracker#IT214_sample_compression" rel="nofollow noreferrer">Resonant filters</a>.</p>
<p><span class="math-container">$$K[n] = aS[n] + bK[n-1] + cK[n-2]$$</span></p>
<p>where:</p>
<p><span class="math-container">... | 922 |
filter design | Digital slew detection | https://dsp.stackexchange.com/questions/83243/digital-slew-detection | <p>I'm looking for an algorithm to detect the slew rate of a 50Hz discrete input signal sampled at 400Hz. I'm doing the obvious - so a low-pass filter on <em>(sample - prev_sample) / deltaT</em> but this results in an oscillating output. I think this is because often the input is zero because <em>sample == prev_sample<... | 923 | |
filter design | FIR filter design with frequency sampling method - setting proper phase response for IDFT | https://dsp.stackexchange.com/questions/19625/fir-filter-design-with-frequency-sampling-method-setting-proper-phase-response | <p>I'd like to implement freuqency sampling method for linear phase FIR filter design using IDFT transform.</p>
<p>My procedure goes like this :</p>
<ol>
<li>determine desired magnitude response value in frequency points</li>
<li>I add linear phase response function with group delay (N-1)/2 to get complex frequency r... | <p>Your procedure is of course correct. It is in the details where things usually go wrong. One important thing is how to extend the desired frequency response beyond Nyquist taking the required symmetry into account. In order for the filter coefficients to be real-valued, the desired frequency response must satisfy</p... | 924 |
filter design | Relation between FIR filter's transition width and phase delay | https://dsp.stackexchange.com/questions/35607/relation-between-fir-filters-transition-width-and-phase-delay | <p>How does the transition width of a FIR filter relate to phase delay at the output of the filter?</p>
<p>I have been trying to find information on the subject for days.</p>
| <p>In <a href="https://dsp.stackexchange.com/a/34307/4298">this answer</a> I gave two well-known heuristic design formulas relating the filter order of (linear-phase) FIR low-pass filters to the transition bandwidth. According to both formulas, the transition bandwidth is inversely proportional to the filter order. Sin... | 925 |
filter design | FIR filter compensator when using a CIC decimation filter | https://dsp.stackexchange.com/questions/160/fir-filter-compensator-when-using-a-cic-decimation-filter | <p>When decimating a narrow-band signal with a <a href="http://en.wikipedia.org/wiki/Cascaded_integrator-comb_filter">cascaded integrator-comb (CIC) filter</a>, which FIR filter is more suitable to compensate the CIC frecuency response?</p>
| <p>There is no single answer to your question: as with any filter-design problem, it depends upon your requirements. As described pretty well on the <a href="http://en.wikipedia.org/wiki/Cascaded_integrator-comb_filter" rel="nofollow">Wikipedia page</a>, CIC (cascaded-integrator-comb) filters consist of a number of pai... | 926 |
filter design | Phase-shift filter design | https://dsp.stackexchange.com/questions/2934/phase-shift-filter-design | <p>If a time-domain signal has sharp corners, its frequency spectrum will contain high-frequency components. Truncating the spectrum results in Gibbs' phenomenon. So if you're trying to design an FIR, you really want the target frequency response to be nice and smooth so that windowing the impulse response down to a fi... | <p>This would be an allpass filter. Except for the trivial case of unity and integer-sample delays, these can't be done as FIR filters and in general an IIR filter is required. However, they are easy to make. The zeroes of an allpass are simply the inverse of the poles (and vice versa). If you have the poles in polynom... | 927 |
filter design | Realtime filtering on a microcontroller, with dynamic cut off frequencies | https://dsp.stackexchange.com/questions/8120/realtime-filtering-on-a-microcontroller-with-dynamic-cut-off-frequencies | <p>Is it possible to dynamically filter a signal in realtime on a microcontroller? </p>
<p>What I mean by dynamically is to change the cut off frequency of the filter on the fly. </p>
<p>I have some DSP knowledge and realize that I probably do not have the computational power to do an FFT on the fly. Instead I should... | <ul>
<li>You can pre-compute the coefficients for a bunch (say $N=1024$) different cutoff frequencies. If your application doesn't need to provide fine control over the cutoff frequency, just read from your table and you're done. This works best if you have a lot of ROM and/or you use short FIR or IIR filters.</li>
<li... | 928 |
filter design | Applying FIR filter to data with different sample rates | https://dsp.stackexchange.com/questions/1104/applying-fir-filter-to-data-with-different-sample-rates | <p>I have a filter design, and it filters over a 1-2 kHz range.<br>
What should I do if I want to apply it to data with a different sample rate than the one for which it was designed?</p>
<p>Let's say it consists of Bessel and Chebyshev filters. How do I find a function that defines each filter's coefficients at an ar... | <p>Since you mention sampling, you are presumably talking of a digital filter.</p>
<p>The cut-off frequency or half-power frequency of a digital filter is
actually relative to the sampling frequency $f_s$. If your digital
filter is passing signals in the $1$ kHz to $2$ kHz range when you
feed it a signal sampled at $... | 929 |
filter design | Audio EQ Cookbook without frequency warping | https://dsp.stackexchange.com/questions/19225/audio-eq-cookbook-without-frequency-warping | <p>The famous <a href="https://www.w3.org/TR/audio-eq-cookbook/" rel="nofollow noreferrer">https://www.w3.org/TR/audio-eq-cookbook/</a> offers a set of [real] biquad filter calculation formulas that generally work fine.</p>
<p>However, when filter's frequency approaches Nyquist frequency the Q (bandwidth) specification... | <p>here is a quick look at how the 5 degrees of freedom for the parametric EQ can be viewed. it's my take on what Knud Christensen of tc electronic came up with about a decade ago at <a href="http://www.aes.org/e-lib/browse.cfm?elib=12429" rel="nofollow">an AES convention</a> and <a href="http://www.google.com/patents... | 930 |
filter design | why the number of filter coefficients in FIR filter has to be an odd number? | https://dsp.stackexchange.com/questions/18413/why-the-number-of-filter-coefficients-in-fir-filter-has-to-be-an-odd-number | <p>I calculated the order of the FIR filter to be 31(N). so, the number of coefficients has to be 32 (N+1). so, I have to increase it to 33 to make it an odd number.</p>
<p>Why the number of filter coefficients is required to be an odd number?</p>
| <p>I think it is about having a linear phase. Having a linear phase is often what you want because it means the delay introduced by the filter will be the same across all the frequency. Then, if you want a linear phase filter, you need to have a symmetrical arrangement of coefficient <em>around</em> the centre coeffici... | 931 |
filter design | Oversampling and decimation: What filter to use? | https://dsp.stackexchange.com/questions/3293/oversampling-and-decimation-what-filter-to-use | <p>I have a sensor producing (more or less) bandlimited data with a cut-off of about 45Hz, with a roll-off and <a href="http://en.wikipedia.org/wiki/Additive_white_Gaussian_noise" rel="noreferrer">AWGN</a>. I have an ADC that samples said signal at 800Hz, with a single-pole anti-aliasing filter at about 200Hz. The prob... | <blockquote>
<p>Should I, for example, do a low-pass FIR filter to squeeze out as close to 50Hz of signal bandwidth as possible?</p>
</blockquote>
<p>Yes, that is exactly what you should do. That is an extremely low data rate, so even with a wimpy processor I would think that should be able to do a pretty good filt... | 932 |
filter design | IIR filter parallelization | https://dsp.stackexchange.com/questions/8020/iir-filter-parallelization | <p>Is there any current ideas about IIR filter algorithm parallelization with thread count greater than filter order?</p>
<p>Ideally, parallelization method should load GPU efficiently.</p>
| <p>You might be interested in the following paper:</p>
<p>Nehab, D; Maximo, A; Lima, R; Hoppe, H: GPU-Efficient Recursive Filtering and Summed-Area Tables. ACM Trans. Graph. 30(6):176 (December 2011). doi://10.1145/2024156.2024210
<a href="http://w3.impa.br/~diego/publications/NehEtAl11.pdf" rel="nofollow">http://w3.i... | 933 |
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