6 votes
Accepted

Doubts on LMS derivation

Here I expected $y(n)$ is to be computed by convolving $x(n)$ with $h(n)$, but in the equation given by Wikipedia it is shown as a matrix multiplication $y(n) = h^H(n).x(n)$. Are these two ...
Peter K.'s user avatar
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4 votes
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Unable to understand the derivation of the update equation for LMS

so with an LMS filter, we have a time-variant $N$-tap FIR filter: $$ y[n] = \sum\limits_{k=0}^{N-1} h_n[k] \, x[n-k] $$ $x[n]$ is the input signal, $y[n]$ is the FIR output, and $h_n[k]$ are the FIR ...
robert bristow-johnson's user avatar
4 votes

Variable Step Size LMS vs Leaky LMS Adaptive Filter Algorithm

Variable step size LMS is generally used to improve the speed of convergence or decrease steady-state error. Leaky adaptation is used to combat problems like the potential instability of the filter in ...
Hooman's user avatar
  • 321
3 votes

Beamformer implementation methods

MVDR and LMS beamformers are two different things. The equation you wrote for the MVDR beamformer is the solution to the "Minimum Variance Distortionless Response" (MVDR) criterion (i.e., $...
Gillespie's user avatar
  • 1,767
3 votes

Implementation of Block LMS

As applesoup says in the comments the term $$ \mathbf{u}(kL+i)e(kL+i) $$ is a vector, not a single value (some integer). Why do you think it's a scalar? To answer your question: no, it's incorrect ...
Peter K.'s user avatar
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3 votes
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Explain the Adaptive Part of Adaptive Algorithms - Kalman Filter and Least Mean Square / Constant Modulus

Adaptive Filters are called "Adaptive" when they can adapt to changes in data. In the filters you mentioned above, which are part of the Linear Filters family the property means their coefficients are ...
Royi's user avatar
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3 votes
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IIR Adaptive Filter in MATLAB

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 ...
megasplash's user avatar
3 votes

Why Wiener filter is not optimal?

The Wiener filter minimizes the MSE under a series of assumptions, which usually don’t match reality. That means that, in practice, it will not give the solution with the smallest MSE possible. Using ...
Cris Luengo's user avatar
  • 2,494
3 votes
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LMS adaptive filter - is it Least mean square or least mean squares?

According this 2005 Stanford reference, "Thinking about Thinking, the Discovery of the LMS Algorithm", in 1960 the algorithm was baptized least mean square. I met Ted for the first time on ...
Brethlosze's user avatar
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3 votes
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Filtered-X LMS algorithm and built-in MATLAB implementation

I think you are mixing the estimated, real and modelled responses. You can kinda safely assume that the real transfer functions $h_{N_{p}}$ and $h_{N_{s}}$ are never known. This, of course, is in the ...
ZaellixA's user avatar
  • 1,288
2 votes

Why is my NLMS filter off by +/- 2?

TL,DR Summary: Your code is in error because of the minus sign on process[0] in the signal generation if statement. Once that is corrected for, the adaptive filter ...
Peter K.'s user avatar
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2 votes
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Stochastic approximation algorithm

The issue is possibly that the input signal you have chosen is not persistently exciting. This means that the signal doesn't "excite" enough modes of the filter in order to be able to accurately ...
Peter K.'s user avatar
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2 votes
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LMS algorithm for modeling step-size ambiguity!

I have the first edition of Behrouz Farhang-Boroujeny's Adaptive Filters book. I found it useful and it was definitely more practical in terms of implementing adaptive filters than other textbooks ...
Michael_RW's user avatar
2 votes

Why does block LMS have the same performance as LMS?

here is a short and little (a.k.a. "consise but terse") derivation of the LMS and normalized LMS adaptive filter. once the LMS has converged on a reasonably stable equilibrium for $h_n[k]$, they won'...
robert bristow-johnson's user avatar
2 votes

what is an alpha filter?

My guess is that it is an alpha filter, as defined in the context of alpha/beta filtering.
Robert L.'s user avatar
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2 votes
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Seperation of wideband and narrowband - Adaptive Filter

A narrowband signal seems like (almost) periodic as indicated by $$ x[n] = m[n] \sin( w_0 n) $$ where the message $m[n]$ has such a low bandwidth that the peak amplitude (the envelope) of the carrier ...
Fat32's user avatar
  • 28.2k
2 votes

estimate the impulse response after equalization

Note that what you're trying to do is equalization, as opposed to channel estimation. If we ignore the noise for the moment then, ideally, the concatenation of the equalizer and the channel (modeled ...
Matt L.'s user avatar
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2 votes

Estimate Instantaneous Frequency Using LMS Algorithm

I make no claim this is optimal and I also do not think that the overshooting you mention is necessarily incorrect. Nothing can change instantaneously, so you are bound to see some range of ...
AnonSubmitter85's user avatar
2 votes

How to calculate EVM in %age of an Equalized Constellation in 16QAM?

The Error Vector is the Euclidean distance from the actual sample at the optimum timing location in each symbol to the actual symbol location in a reference constellation (as the distance to closest ...
Dan Boschen's user avatar
2 votes
Accepted

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

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 ...
jithin's user avatar
  • 2,263
2 votes

How to evaluate fixed-point implementation of LMS filter is correct?

I'm not an expert on the LMS algorithm. Perhaps you should add a link to the algorithm description so we can help you. However, I have adapted a lot of algorithms to fixed-point implementation, so I ...
Ben's user avatar
  • 3,777
2 votes

LMS filter always diverges on Cauchy data?

What would you like it to converge to? I ask, because the Cauchy Distribution has no mean that's well-defined, nor finite variance; the covariance between two (or many) Cauchy variables isn't defined, ...
Marcus Müller's user avatar
1 vote

How to calculate EVM in %age of an Equalized Constellation in 16QAM?

From my experience EVM is defined as $$ EVM = \sqrt{\frac{1}{NP_{avg}}\sum_{n=0}^{n=N-1}(|x_n-x^*_n|^2)}\\ EVM_{\%} = EVM \times 100 $$ where $x_n$ is the equalized symbol, and $x^*_n$ is the ...
jithin's user avatar
  • 2,263
1 vote
Accepted

Unknown symbol/expression in text about adaptive filters (cst)

The standard normalized step-size LMS algorithm computes the current step-size according to $$ \mu = \frac{c}{s_k^T \cdot s_k} $$ where $c$ is a suitable scale factor and $s_k^T \cdot s_k$ is the ...
Fat32's user avatar
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1 vote
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Can Temperature Data be Predicted Using Adaptive Filter (Such As LMS) Algorithm?

Yes you can predict future temperatures, based on past temperatures, using adaptive filtering as well. The optimal linear estimation of a WSS random process from its past values, which is known as ...
Fat32's user avatar
  • 28.2k
1 vote

Recursive Least Square Adaptive Linear Equalizer

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 ...
Dan Boschen's user avatar
1 vote
Accepted

Fair performance comparison betweem LMS & NLMS

For fair comparison of one algorithm to another, the value of step size does not need to be same. You can adjust the step sizes of both algorithm so that the mean-squared-error learning curves base ...
Faizan Zaheer's user avatar
1 vote

Block LMS with overlapping blocks

There is no hard rule regarding convergence speed of the block-LMS vs sample-by-sample LMS. It really depends on the scenario. On top of my head is the following two (stationary) scenarios: A very ...
M.Halimeh's user avatar
1 vote
Accepted

Equalizer coefficients and channel coefficients

With a blind equalization technique like the constant modulus algorithm (which is often implemented using a least mean squares (LMS) filter as you indicated), you aren't directly estimating the ...
Jason R's user avatar
  • 24.6k

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