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Two meanings for "innovation" in Wiener filter are the same?

This is related question to A question about Wiener filter based on Linear Estimation by Kailath, based on the textbook Linear Estimation by Kailath. In that link I talk about how I first learned what ...
monad's user avatar
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A question about Wiener filter based on Linear Estimation by Kailath

In my linear estimation class based on the textbook Linear Estimation by Kailath, we went through the process of finding LLSE of $\hat{x}(t+\lambda)$ for fixed $\lambda$ given $\{y(\tau)|-\infty<\...
monad's user avatar
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Wiener Filter for Noise Reduction in GPS Sensor Measurement

I am getting position and velocity measurements out of a GPS sensor and I want to filter these data, so I can have a better, less noisy, estimation of the true measurements. I thought of doing this ...
useeeeer132's user avatar
3 votes
0 answers
105 views

Implementing a non-causal Wiener filter

I'm attempting to implement a non-causal Wiener filter for removing additive white noise from a measured signal. I've had some trouble and I have reduced my problem to a demonstration on simulated ...
Marc's user avatar
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Confused About Relationship Between Number of Points and Solving Wiener Filter Coefficients in Time Domain vs Fourier Domain

I'm interested in computing M, FIR filter taps / coefficients using a Wiener filter approach with known signal and noise timestreams. I know of two ways to compute the coefficients: one in the Fourier ...
Jenny Smith's user avatar
1 vote
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41 views

Proof that the estimation error in the LMS filter is uncorrelated

I need to demonstrate that the estimation error in the LMS adaptive filter is white. The LMS equations are the following: $y(n)={\mathbf{\hat{w}}}(n)^H\mathbf{u}(n)$ $e(n)=d(n)-y(n)$ ${\mathbf{\hat{w}}...
Andrea Tani's user avatar
0 votes
1 answer
83 views

Numerical Stability for Channel Estimation

In this post: Compensating Loudspeaker frequency response in an audio signal I derive the Wiener-Hopf equations for least squares equalization (and channel estimation if we swap Tx and Rx) from the ...
Dan Boschen's user avatar
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4 votes
1 answer
171 views

The Different Solutions for Filter Coefficients Estimation for Periodic Convolution and Full Convolution

As a continuation of the question Least Squares Solution Using the DFT vs Wiener Hopf Equations raised by Dan Boschen. The question is, given the model: $$ \boldsymbol{y} = \boldsymbol{h} * \...
Royi's user avatar
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9 votes
4 answers
668 views

Least Squares Solution Using the DFT vs Wiener-Hopf Equations

Least Squares channel estimation (or equalization) can be accomplished using the "Wiener Hopf Equations", or the Discrete Fourier Transform. Both appear to be least squares solutions. How do ...
Dan Boschen's user avatar
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1 vote
1 answer
52 views

Basic audio denoising in the frequency domain using minimum statistics?

I'm trying to do some example elementary denoising of the audio signal. Let's say input is speech with constant traffic background noise. First I calculated block-based overlap-add Fourier transform (...
Danijel's user avatar
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1 answer
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Trying a wiener noise cancellation code but not able to filter out the noise

I am performing noise cancellation using Wiener filter for a project. The project statement is "to record our voice and take it as desired signal, add a noise, use wiener filter to estimate the ...
Kuchi Yashwanth's user avatar
2 votes
0 answers
54 views

Deconvolving while suppressing other known signals

Given a known impulse response $h(t)$ and an observed signal $y(t)=(h*x)(t)+n(t)$, my aim is to recover an estimate of $x(t)$ in the presence of unknown additive noise $n(t)$. If the mean power ...
Museful's user avatar
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3 votes
1 answer
166 views

Difference between lattice and wiener FIR filter

I know the structure of lattice and wiener filter. But I though FIR filter is always FIR (wiener, tap + delay) filter, But what is the advantage of lattice structure, which in the CMSIS DSP filter ...
mohammadsdtmnd's user avatar
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84 views

Wiener filter for vector-valued signal

I'm trying to understand the derivation of a Wiener filter for a vector-valued signal, found in the paper "Kalman filtering in non-Gaussian model errors: a new perspective," IEEE Signal ...
Rodney Price's user avatar
5 votes
2 answers
1k views

Can the deconvolution Wiener filter reduce noise without having a blurred image?

I am trying to denoise many several noises with several filters for a research i have, i found a deconvolution Wiener filter made by "mr.tranleanh" on Github, as you can see here . what I ...
kode224's user avatar
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1 answer
427 views

EVM reduction for GNU Radio GMSK quadrature demod using Wiener equalizer

I have been exploring different ways of improving the EVM performance of quadrature demod block for GMSK demodulation. As we all know, the Gaussian filter introduces intentional ISI, which can be ...
Moses Browne Mwakyanjala's user avatar
1 vote
1 answer
414 views

Does BM3D really need the noise power spectrum beforehand?

I'm at the moment trying to implement a neural network which uses BM3D as a preprocessing step. The problem is, when using the python implementation of BM3D from the paper Collaborative Filtering of ...
Gabriel Oliveira's user avatar
1 vote
1 answer
279 views

Signal values explode when filtering with bandpass and wiener in Python

I have a five second audio (speech with background noise), which I want to process first with bandpass filter and then with wiener filter to reduce noise. Audio is normalized between [-1, 1] and I ...
Xarzaloxa's user avatar
4 votes
1 answer
1k views

Why Wiener filter is not optimal?

I am investigating Wiener filter in the frequency domain, given by $$ W(\omega) = \frac{S_{ud}(\omega)}{S_{uu}(\omega)}$$ where $S_{xy}(\omega)$ is the cross-power spectral density (CPSD), see scipy....
Triceratops's user avatar
1 vote
1 answer
57 views

What is $S$ in the Wiener filter exactly?

I am reading about the Wiener deconvolution in Wikipedia. In the expression of $G$ we have $$G=\frac{H^*S}{|H|^2S+N}$$ where $S = \mathbb{E}|X|^2$. Why do we have the $\mathbb{E}$ symbol? Isn't $X$ a ...
user171780's user avatar
5 votes
1 answer
87 views

Estimate the Image Using Multi Realizations of Its Convolution with a Known Filters Using Wiener Filter

Suppose we have a corrupted image $Y = H*X + \epsilon$ formed by taking an image $X$, convolving it with a point-spread function $H$, and adding gaussian noise $\epsilon$. Then we know that the Wiener ...
Sunay Joshi's user avatar
1 vote
1 answer
2k views

Find coefficients of optimal Wiener filter of length 2

I need to find the coefficients (impulse response) of a FIR Wiener filter with length equal to 2. I have a gaussian white noise signal that is generated using the Standard Normal Distribution (mean = ...
jmc11's user avatar
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2 votes
1 answer
98 views

Basic Wiener application

I'm trying to filter this $g(x,y)$ WGN added image My Wiener filter is: $$H(u,v) = \frac{P_{f}}{P_{f}+P_{n}}$$ Where the image power spectral density $P_{x}$ is estimated as $\frac{|X(u,v|^{2}}{N^{2}}$...
Pasta Addict's user avatar
1 vote
1 answer
694 views

Real Data Complex Transfer Function using H0, H1, H2 Estimators

BACKGROUND: This question is attempting to consolidate material discussed in two previous topics. These are: Understanding the H1 and H2 estimators @Pontus S Frequency-domain deconvolution: "...
telemeister's user avatar
5 votes
2 answers
447 views

Wiener filtering/deconvolution for non-stationary noise

Consider a stationary discrete-time random process $x[k]$ which undergoes low pass filtering by a filter with impulse response $h[k]$ and is subject to additive, temporally uncorrelated noise $n[k]$ ...
rhz's user avatar
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6 votes
2 answers
1k views

What is the advantage of Wiener filter for noise reduction of a 1D signal?

I have a 1D signal, acquired by an accelerator sensor that measure the vibration of a structure. What is the advantage of using a Wiener filter for noise reduction compared to the other (more classic) ...
EmThorns's user avatar
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10 votes
2 answers
242 views

Does the Wiener Filter Achieve the Cramer Rao Lower Bound (CRLB)?

I have been told (Wikipedia agrees) that the Wiener filter is optimal when signal and (additive) noise are WSS. Optimal in the sense that it minimizes the mean-square error. The Cramér–Rao bound is ...
Fabian's user avatar
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1 vote
1 answer
456 views

IIR Adaptive Filter in MATLAB

Suppose I have a IIR filter represented by $$G_0\left(z\right)=\frac{1}{1-0.2z^{-1}-0.1z^{-2}}$$ I would like to use the LMS algorithm to model an FIR filter $G\left(z\right)$ of order $N = 15$ such ...
JordenSH's user avatar
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2 votes
0 answers
362 views

Find the Autocorrelation and Cross Correlation of The Wiener Filter

I am dealing with a problem with Wiener filter. Assume the original function is $s(t)$ with observation $x(t) = s(t) + n(t)$. And $s(t)$ and $n(t)$ are WSS (wide sense stationary) and they are ...
stander Qiu's user avatar
3 votes
1 answer
367 views

The Wiener Filter for the Time Derivative of the Signal

Assume the observation of the original signal $s(t)$ is $x(t) = s(t) +n(t)$, where the signal and noise are independent. Then we need to design the Wiener filter $g(t)$ to estimate $\frac{d s(t)}{dt}$ ...
stander Qiu's user avatar
1 vote
1 answer
361 views

Finding the Correlation Matrix of Wiener Filter using MATLAB

I have the problem below and need to solve it using Matlab. I not a big expert in Matlab and just don't know how to implement it. Basically, it says that \begin{equation} R\:=\:\left[X\left(n\right)X^...
JordenSH's user avatar
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0 answers
157 views

finding power spectral density from a vector

I have been given a vector: \begin{equation} v= \:\begin{pmatrix}\frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix} \end{equation} my job is to find the power spectral density from this vector \...
JordenSH's user avatar
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2 votes
1 answer
163 views

Channel equalization affect on input signal

I have the following problem. Am trying to understand how the channel block affects the input signal s(n). I know that x(n), the input signal to the filter is basically: \begin{equation} x\left(n\...
JordenSH's user avatar
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1 vote
1 answer
372 views

Where does the "Desired Response" come from in a Wiener filter?

I'm confused right off the bat in the introduction to Wiener filters, because how can you know what the "Desired response" is? Where does it come from? And if you know it already, then why build a ...
j03y_'s user avatar
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0 votes
1 answer
111 views

How can I plot Wiener filter's behaviour for different taps (memory filter)?

What's the expected behaviour of Wiener Filter for different taps (memory filter) , when input signal is a sinusodial tone? Do you have any idea how I can plot or simulate Wiener Filter's behaviour (...
estamos's user avatar
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6 votes
1 answer
765 views

Transfer function and deconvolution

Forewords This question is about methodology references and numerical application. I am posting on Signal Processing because I think this question belong to this place. I am new to the stack, feel ...
jlandercy's user avatar
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6 votes
2 answers
1k views

Basic Questions on Wiener Filtering

I read a lot about Wiener Filters (focusing on discrete time case). I understand the math, but I am quite disconnected from the real life assumptions behind using such a filter. Unfortunately ...
Cowboy Trader's user avatar
1 vote
1 answer
786 views

Why Wiener filter not IIR

I would like to limit discussion to discrete time causal Wiener filter. By definition it is an FIR filter, and it also has optimality under Mean Square Error criterion within the class of linear ...
Cowboy Trader's user avatar
1 vote
1 answer
115 views

Is there a hypothetical situation where once can use Wiener filter prior Matched filter to get better result?

Is there a hypothetical situation where once can use Wiener filter prior Matched filter to get better result? Mostly I am looking for an example or a situation where both the filters are required as ...
Creator's user avatar
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4 votes
2 answers
78 views

Intuition about independent signals

Given is this Wiener filter: From this we take \begin{equation} x[k]-a x[k-1]=v[k] \end{equation} $v(k)$ is assumed to be a white gaussian noise. In the textbook it is then stated that The ...
Mr.Sh4nnon's user avatar
3 votes
1 answer
1k views

Why is White Noise so important in System Identification or Adaptive Filters

I'm looking to implement a feedback cancellation filter using Wiener Filtering, where an adaptive Wiener filter is used to cancel the feedback occurring in the path between a loudspeaker and a mic (...
Aditya TB's user avatar
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10 votes
2 answers
4k 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 ...
Ηλεκτρολόγος Μηχανικός's user avatar
0 votes
1 answer
1k views

Wiener Filter in Frequency Domain: What it does to a specific Frequency?

As I understand Wiener filter in time domain tries to estimate a signal as close as possible to its (original) non-degraded signal using the degraded signal by white noise. $$H(\omega)=\frac{\Phi_{...
Daki Withanage's user avatar
6 votes
3 answers
908 views

Question on Wiener Filtering

I have read that a Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process. Now, my doubt ...
Curiosity's user avatar
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1 vote
0 answers
2k views

Python scipy.signal.wiener filter for speech processing

As far as I know Wiener filter can be used in Image processing.I wonder that if i can use Python scipy.signal.wiener() for speech processing as well. Thanks in advance.
Umur Togay Yazar's user avatar
0 votes
1 answer
693 views

Wiener deconvolution in cpp giving back the same image

I was trying to deblur a noisy image using wiener deconvolution. I found this code which added noise to an image and removed it as well. Modifying this code only i tried to implement the exact formula ...
Vaibhav Setia's user avatar
0 votes
2 answers
272 views

How to estimate ALL time-delays across MULTIPLE signals?

Imagine there are 100 recordings of the same signal or pattern, but those recordings are not properly aligned with each other in time. In other words, each sample has some unknown time delay in ...
Robert's user avatar
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2 votes
1 answer
405 views

Wiener Filter Additive Noise Uncorrelated

I have been trying to understand for a while now why a non-causal Wiener filter that has a frequency response of the type H(jω)=S_yx(ω)/S_xx(ω) where ...
Adrian Guerra's user avatar
1 vote
1 answer
634 views

Solving Wiener Hopf integral equation for causal filter of predictor

Given a stochastic signal $x(t)$ with autocorrelation function $R_{xx}(\tau)=\mathrm{exp}(- \alpha|\tau|)$, $\alpha>0$. I want to predict $x(t+\lambda)$,$\lambda>0$ by $x(t-\tau)$, $\tau\ge0$ ...
Rikeijin's user avatar
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1 vote
0 answers
103 views

Wiener filter modeling

What would happen if we changed the input with the output in the Wiener filter computations? When we are designing a filter we use the input and the desired response vectors to find the Wiener filter. ...
user31317's user avatar