An adaptive filter is a filter that self-adjusts its transfer function according to an optimization algorithm driven by an error signal.

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### Should the input of a Kalman filter always be a signal and its derivative?

I always see the Kalman filter used with such input data. For example, the inputs are commonly a position and the correspondent velocity: $$(x, \dfrac{dx}{dt})$$ In my case, I only have 2D ...
272 views

### Using an error prediction filter for filtering a semi-known signal

I'm trying to wrap my head around the proper use of a Wiener or error-prediction filter for filtering data. It seems to me that it is only a whitening filter, so how is it used when the data you want ...
708 views

### How to Improve Least Means Squares (LMS) / NLMS Filter Performance?

Are there ways to increase computational performance of a normalized least squares (NLMS) filter? Multidelay block frequency-domain (MDF) filters have been proposed to do this, but they also take away ...
6k views

### What does an adaptive filter do?

I studied a bit about adaptive filter on internet and found that its a special filter which keep on updating its filter value as soon as it proceeds. It finds out the difference between input and ...
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Adaptive IIR filters is not straightforward, and may be unstable. Many people say that adaptive IIR filters use less coefficients than FIR filters. What I'm curious about is how many coefficients can ...
436 views

### Why does over-modelling an adaptive AR NLMS filter fix sharp spikes?

I just simulated an auto-regressive second-order model fueled by white noise and estimated the parameters with normalized least-mean-square filters of orders 1-4. As the first-order filter under-...
2k views

### Difference between 'conventional' and 'adaptive' beamformers?

This might be a terminology question but I am not sure. Basically, what is the difference between conventional beamformers, and adaptive beamformers? I thought that all beamformers were inherently ...
186 views

### For complex values, why use complex conjugate in convolution?

Taken from Adaptive Filter Theory (2014) written by Haykin page 110 : $$y(n) = \sum_{k=0}^{\infty} w_k^*u(n-k), \quad n=0,1,2,...$$ where $u$ and $w$ are complex values. My question is why use ...
700 views

### Adaptive filtering: Optimum filter length and delay

I'm trying to find the optimum filter length for an Adaptive Filtering, using RLS Algorithm. I'm using this design: So the "error" signal is the signal without noise (and that's the signal that I ...
2k views

### What is the difference between the Weiner-Hopf equation and the normal equation?

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 ...
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I found algorithms that seems the same to me, but they are described with different names (in field of adaptive filtering). For example: LMS - least-mean-squares seems to be GD - stochastic gradient ...
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Does anyone know about different adaptive filtering implementations (LMS, RLS ...) in 2D or even 3D ? I have sequences of 2D images and 3D volumes with repeating patterns but small differences. I was ...
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### Relative performance of RLS and LMS filters

It's known that the RLS filter converges faster than the LMS filter in general, but that if you're tracking time varying parameters the LMS algorithm can perform better. My question is under what ...
183 views

### Regression vector size for prediction, reconstruction and filtration with adaptive filters

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. ...
846 views

### Image Processing: Flatten a 3D Ball

There are many descriptions of how to turn a 2D image into a 3D one, however I want to do the opposite, in particular to a ball. As an example, consider the following ball: If only the (relatively) ...
1k views

### Are there any open source libraries for Adaptive noise cancellation?

I'm creating a chat application where people can input text via speech and I need to implement noise cancellation using Adaptive noise cancellation technique. I'm using dual microphones for this ...
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### Echo cancellation supporting long delays and without frequency domain processing

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 ...
81 views

### Are all least square filters adaptive?

Are least square filters, or filters that minimize error energy, the same as least mean square adaptive filters?
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### Doubts on LMS derivation

I have been trying to follow the Least Mean Square(LMS) algorithm derivation given by Wikipedia here and have the following questions. Here I expected $y(n)$ is to be computed by convolving $x(n)$ ...
408 views

### Adaptive equalizer for IIR channel?

I am quite new to the idea of equalization. I have a few queries regarding the same. In my application I require to equalize a channel whose impulse response is an IIR response. Is it possible to ...
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### MATLAB : Proper estimation of weights and how to calculate MSE for QPSK signal for Constant Modulus Algorithm

I had asked conceptual Question about Constant Modulus Algorithm. I am implementing the simple steps of the algorithm, as I do not have the cma() built in module. ...
393 views

### Frequency tracking with huge noise

I'm working on a frequency tracking problem with noise, where the amplitude of the noise is orders of magnitude higher than the amplitude of my signal (~1000x). Some details: The signal is roughly ...
528 views

### How to include phase in a sinusoidal Kalman Filter

I start with the equation for sinusoidal motion with an offset and differentiate to get the 2nd order ODE describing the motion of the object. \begin{align} x &= A\sin(\omega t + \phi) + O\\ \dot{...
129 views

### Correction of a signal through a transmitter

I am inquiring as to a practical way to solve a problem I have. Basically, I need to transmit a signal, $x[n]$, through a seismic transmitter. (It will go through a D/A, etc). The transmitter that ...
249 views

### Why does block LMS have the same performance as LMS?

The block LMS and conventional LMS have the same convergence rate and the same misadjustment. I am having trouble wrapping my head around this. The block LMS uses a more accurate estimate of the ...
509 views

### Phase noise estimation and compensation schemes

Brief background There is a known problem that high order modulation schemes suffers from phase noise of reference generator. It's very important issue for e.g. line-of-sight (LOS) modems exploiting ...
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### Least Mean Squares (LMS) Filter Weight Update

I have a general question regarding Least mean squares adaptive filters. Using the example of noise cancellation, I understand that if you have a set of reference signals (S) and corrupted signals (S+...
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### Removing low frequencies from a signal

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 ...
140 views

### Bandpass filter that automatically adapts its bandwidth when a transient is detected (to avoid to smoothen the transient)

Let's say we want to isolate a band 1000 hz +/- 50 hz. Obviously, limiting the bandwidth by applying a passband filter will always destroy a bit the sharp transients (a Dirac or a rectangular ...
188 views

### Covariance matrix of an adaptive filter input

I run many times in equations containing the trace of covariance matrix of an adaptive filter input. But it is not really clear what it is. For example in this paper the input covariance matrix is ...
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The quadratic performance surface of an adaptive filter is a paraboloid. Its minimum can be found wherever the gradient is zero. However, since there are two types of paraboloids (elliptical and ...
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### What are the Elements of Filters for Highly Volatility Price Series with Jumps?

What are the best filtering techniques for a highly volatility price series with jumps. What needs to be considered in designing new filters for practical finance which are adaptive and highly ...
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### Seperation of wideband and narrowband - Adaptive Filter

I have the following diagram for the adaptive seperation of a narrowband and wideband signal using LMS algorithim, The way it was explained to us was that "The narrowband signal is correlatied over ...
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### Finding the auto-correlation sequence $r_{xx}[k]$ for an AR(2) process

Consider the following recursive difference equation of a LTI system, where $v[n]$ is a white noise, zero-mean process with $\sigma_v^2 = 1$. $x[n] = v[n] + 0.75x[n-1]-0.25x[n-2]$ I want to ...
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### How to Subtract One Signal from Another?

I am capturing some body internal signals. I am using 2 identical mics. One captures the in body signal and one open air. I want to remove/delete/subtract the open air signal (noise for me) from ...
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### Is there a widely available implementation of an adaptive, recursive, numerically stable IIR filter?

I need to identify the coefficients of a linear, causal, time-invariant physical system that can be described by a classical state-space formulation. For the sake of the example, suppose that the ...
366 views