## Forums Search for: Autocorrelation

## Does perfect white noise really exist?

inA simple question: Based on the classical definition of "White Noise" (a random process which has zero autocorrelation, and a purely flat...

A simple question: Based on the classical definition of "White Noise" (a random process which has zero autocorrelation, and a purely flat PSD from -INF to +INF), measurement of white noise to determine these properties (rxx, PSD, mean, variance, skewness and kurtosis) poses a paradox: When we measure "pure white noise", we ise a band-limited measuring device (such as a spectrum analyzer), ...

## Karhunen-Loeve and Transform-Domain LMS Algorithm

inDear readers, my question is on something that looks like a variation of the Karhunen-Loeve Transform. The normal Karhunen-Loeve Transform...

Dear readers, my question is on something that looks like a variation of the Karhunen-Loeve Transform. The normal Karhunen-Loeve Transform would be like this: for a signal u of length L and an adaptive FIR filter of order M, we compute the Autocorrelation Matrix and its eigenvectors. In Matlab: L=max(size(u)); ruu=xcorr(u,u)/L; M=16; Ruu=toeplitz(ruu(L:L+M-1)); % Correlation Matrix...

## Basic Question about the PSD

inHi I am plotting the PSD using Wiener-Khintchin theorem (1). I recall from my signal processing course the the fourier transform is periodic...

Hi I am plotting the PSD using Wiener-Khintchin theorem (1). I recall from my signal processing course the the fourier transform is periodic with peroiod of 2 pi. Should the PSD be periodic since the wiener-khintchin theroem is essentialy a fourier transform? What should the perido be in general? PSD(f)=4*Integral[cos(2*pi*f*t)*Autocorrelation from -inf, +inf] (1) thanks!!

## Symmetric Wiener Filter

inHi all, I have an exercise, and i should compute the wiener-hopf equations for a symmetric zero phase wiener filter. I have started from the...

Hi all, I have an exercise, and i should compute the wiener-hopf equations for a symmetric zero phase wiener filter. I have started from the fact that the symmetry and the zero phase imply h[n]=h[-n] for the coefficients of the filter and I compute the following equation sum{h(l)[Rx(k-l)+Rx(l-k)+Rx(k+l)+Rx(-k-l)]}=Rxs(k)+Rxs(-k), where l=0,...,N , k=0,...,N Rx is the autocorrelation Rxs is t...

## Encoding residual (LPC on speech signal)

inHi, As part of my research project, I'm working on vector-quantization applied to an LPC-like encoding scheme. For each frame of speech...

Hi, As part of my research project, I'm working on vector-quantization applied to an LPC-like encoding scheme. For each frame of speech (I tentatively put a frame length of 128 samples -- at 8kHz sampling rate), I compute the optimal prediction filter (using the autocorrelation method), and then apply that filter to the signal (well, I apply 1-P to the signal, where P(z) is the optima...

## Multichannel (MISO) Wiener filter design

inProblem: Design one wiener filter that best matches a time snapshot of data taken from multiple channels of equal interest, that is, the domain...

Problem: Design one wiener filter that best matches a time snapshot of data taken from multiple channels of equal interest, that is, the domain of the signal is 2D, specifically with # of time samples > > # channels. Think of a window in a grey scale 2D image. The Easter bunny tells me one approach is: 1. Average the autocorrelation matrices for each channel 2. Average th

## detection of primary synchronization signal in LTE

Hi All, According to LTE frame structure every frame have primary synchronization signals.And for primary synchronization signal...

Hi All, According to LTE frame structure every frame have primary synchronization signals.And for primary synchronization signal zadoff- chu sequence is used beacuse of its good periodic autocorrelation as well as periodic cross correlation properties. I thought of using noncoherent correlation in time domain.I tried this method in matlab and seems working for me. My problem is it...

## Wiener Hopf Equalizer delay

inCONTEXT:********************** Transmit x(n) receive y(n). Wiener-Hopf (MMSE) FIR Equalizer is... w = inv(Ryy)rxy where Ryy is the received...

CONTEXT:********************** Transmit x(n) receive y(n). Wiener-Hopf (MMSE) FIR Equalizer is... w = inv(Ryy)rxy where Ryy is the received signal autocorrelation and rxy is the channel input-output crosscorrelation: rxy(k) = E(x(n-D)y(n+k)). The D is a delay parameter chosen to make sure the equalizer is causal. It specifies the location of the impulse of the equalized channel. QUESTIO...

## taking Fourier Transform of random signal vs. taking PSD of random signal?

inHi all, These two terms from two different domain confused me a lot. FT is for deterministic analysis, whereas PSD is the FT of the...

Hi all, These two terms from two different domain confused me a lot. FT is for deterministic analysis, whereas PSD is the FT of the autocorrelation function, which is for stochastical signal analysis... Am I right? I am wondering if we use Matlab generate some random signal, and treat it as a dterministic signal, and take its FT, versus using Matlab to take its PSD, Should these...

## Simulation of symbol synchronization in a OFDM receiver

Dear all I am doing a block for a OFDM receiver that receives as input the ofdm received signal and gives as output a rectangular signal...

Dear all I am doing a block for a OFDM receiver that receives as input the ofdm received signal and gives as output a rectangular signal (for synchronization) in which each pulse represents a peak in the autocorrelation function realised over the ofdm received signal. How can i define a threshold to detect this peak of the correlation function? Is there another way to do this? I will use di...

## PSD vs. Fourier transform

inHello, I have a confusion regarding Fourier transform of a time signal and the PSD. By definition, power spectral density (PSD) is the Fourier...

Hello, I have a confusion regarding Fourier transform of a time signal and the PSD. By definition, power spectral density (PSD) is the Fourier transform of the autocorrelation function. Suppose my time-domain signal is a voltage signal. I sample this at the correct rate, and taking the Fourier transform gives me the maginitudes of of various frequency components present in the signal (with...

## In reality, how do people measure autocorrelation function?

inHi all, I heard tht white noise can be used to do system identification: finding the impulse response of an LTI system: generate a white...

Hi all, I heard tht white noise can be used to do system identification: finding the impulse response of an LTI system: generate a white noise x(t), and then input it to a system h(t), measure the output y(t), then find the R_yx(t), this is in fact the system impulse response h(t)... I understand this by showing it mathematically, yet I want to know what do people do in reality? How ...

## Power Spectrum from Autocorrelation vs. FFT

inI have two questions: 1) Is there a difference b/w the terms 'power spectrum' and 'power spectral density'? They both seem to indicate power...

I have two questions: 1) Is there a difference b/w the terms 'power spectrum' and 'power spectral density'? They both seem to indicate power vs. frequency. 2) Suppose you are given a random sampled data sequence x[n], and you have to find its power spectrum. - Can we find the spectrum by taking the FFT of x[n] and squaring its magnitude? - Can we find the spectrum by taking the FFT of...

## power spectrum via autocorrelation of broken data time series

inHi, I think I understand the basic ideas of spectral analysis but I still have no good feeling how to improve. My problem is that I have data...

Hi, I think I understand the basic ideas of spectral analysis but I still have no good feeling how to improve. My problem is that I have data that is broken every 3 minutes for about 20seconds. In order to generate a power spectrum I try several attempts of simulated data to see what will be the best. I know that the power spectrum should be a power law. So I generate a random time series by dra...

## sqrt in time - effect in freq?

inThis relates to an earlier post - "filter of amplitude versus filter of (I,Q)?". I would like to learn what is the effect in the frequency...

This relates to an earlier post - "filter of amplitude versus filter of (I,Q)?". I would like to learn what is the effect in the frequency domain of taking the square root of a quantity on the time domain. Also, of taking the square (actually magnitude of a complex number) in the time domain? I think I know the second - the magnitude is number*complex_conjugate which is autocorrelation ...

## power spectral density of WSS process question

inHi all, I have a problem which I can't find any way to go: X is an Wide Sense stationary process. Its power spectral density S(w) is zero...

Hi all, I have a problem which I can't find any way to go: X is an Wide Sense stationary process. Its power spectral density S(w) is zero outside [-wmax, wmax]. They ask to prove R(0)-R(t) < 0.5 *wmax^2 *t^2 *R(0). where R(t) is autocorrelation of X. The question is a hint |sin(x)|

## how to pass a random process through a non-linear system?

inHi all, I understood how to pass a stationary random process through a LTI syste... the autocorrelation of the output has a beautiful...

Hi all, I understood how to pass a stationary random process through a LTI syste... the autocorrelation of the output has a beautiful relation with the input's autocorrelations, and so does the power spectrum density... But what if my stationary zero mean Gaussian random process x(t) go through a non-linear system, for example, a signum device(output 1 for input x(t)> 0 and output -1

## How to compute the autocorrelation matrix of a random vector in matlab?

inI want to use matlab to compute the autocorrelaton matrix of a random vector. Here is the code I have written. Is it correct? clc; vec_num =...

I want to use matlab to compute the autocorrelaton matrix of a random vector. Here is the code I have written. Is it correct? clc; vec_num = 1000; x = zeros(8,vec_num); for i=1:vec_num x(:,i) = round(randn(8,1)*10); end total_matrix = zeros(8,8); for i=1:vec_num for j=1:vec_num total_matrix = total_matrix + x(:,i)*x(:,j)'; end end total_matrix = total_matrix / (...

## Fixed-point implementation of levinson durbin algorithm

inHi, Any links to a fixed point implementation of the Levinson Durbin algorithm ...something like this: void levdur(pLpcCoeff, pAutoCorr,...

Hi, Any links to a fixed point implementation of the Levinson Durbin algorithm ...something like this: void levdur(pLpcCoeff, pAutoCorr, pReflec, nOrder) where pLpcCoeff is a pointer to the lpc coefficients where pAutoCorr is a pointer to the autocorrelation coefficients (range -40 to 40) where pReflec is a pointer to the reflection coefficients where nOrder is 10 The autocorrelat...