Questions tagged [autocorrelation]

Autocorrelation is the cross-correlation of a signal with itself.

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31
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1answer
7k views

Does the autocorrelation function completely describe a stochastic process?

Is a stochastic process completely described by its autocorrelation function? If not, which additional properties would be needed?
9
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1answer
2k views

What is an AMDF?

The wikipedia page for Average Magnitude Difference Function/Formula (AMDF) appears to be empty. What is an AMDF? What are AMDF's properties? What are AMDF's strengths and weaknesses, as compared ...
47
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4answers
42k views

What is the difference between convolution and cross-correlation?

I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ. What is the difference between ...
12
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4answers
18k views

Efficiently calculating autocorrelation using FFTs

I'm trying to calculate an autocorrelation on a platform where the only accelerated primitive I have available is the (I)FFT. I'm having a problem though. I prototyped it in MATLAB. I am, however, ...
12
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4answers
2k views

Recommendation for book - Writing DSP code in C

I am looking for some good book, that simply show how you actually write a code in C, to do all the main DSP methods . FFT. Low-pass and high-pass filters. Auto-correlation. Noise processing. And ...
11
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2answers
7k views

Covariance vs Autocorrelation

I'm trying to figure out if there is a direct relationship between these concepts. Strictly from the definitions, they appear to be different concepts in general. The more I think about it, however, ...
2
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1answer
4k views

variance in the time domain versus variance in frequency domain

Hi All: I'm trying to better understand the connection between variance of a time series and the integral of the spectral density over all frequencies. Rather than going through all of the relations, ...
12
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4answers
12k views

How to 'whiten' a time domain signal?

I am trying to understand how exactly to implement what is known as a 'pre-whitening' filter or simply a 'whitening' filter. I understand that the purpose is to make it have a delta as its ...
6
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4answers
7k views

Conceptually, how does a Fourier transform differ from an autocorrelation?

I realize the two are derived using different algorithms, and the units are different, but from a conceptual standpoint of the information they provide how do they differ? I'm thinking here about the ...
4
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1answer
1k views

Autocorrelation of the product of deterministic and random signal

I was wondering how to calculate the autocorrelation of a deterministic signal $x(t)$ multiplied by a stochastic process $M(t)$, whose autocorellation $R_M(\tau)$ is known a priori. In my case, $x(t)$ ...
1
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1answer
88 views

What exactly does compression say about correlation of data?

I've been using the following formula on various empirical data $d$, to obtain a correlation factor $c_f$:- $$ c_f = { |C(d_s)| \over |C(d)|} $$ where $C$ is a compression function like bz2 or zip, ...
2
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1answer
1k views

Random process $X(t)$ with autocorrelation function given find the mean and the variance

Autocorrelation function is $$R_{xx}(\tau)=\frac{20}{1+2\tau^2}$$ So at $\tau=0$$$R_{xx}(0)=20=E[X(t)X(t)]=E[X^2(t)]$$ The variance is $$\mathrm{Var}[X(t)]=E[X^2(t)]-E^2[X(t)]=20-E^2[X(t)]$$ As $X(t)$...
2
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1answer
1k views

Autocorrelation of power spectrum

Anyone have an idea of how I can implement autocorrelation of power spectrum of one image? I tried using: autocorrel = ifft( | fft(power spectrum) | ^ 2 ); but ...
1
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0answers
258 views

Train Pulse Recognition in Medium Voltage Networks

I just started a project in the Smart Grids area. It involves the recognition and quick extinction of earth faults in a medium voltage system. The system works automatically and pretty much gets rid ...
0
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1answer
473 views

What kind of filter I should use to remove the oscillations in this autocorrelation function?

I have an autocorrelation function which is shown as following, I do believe these trailing oscillating wigs are spurious and should be removed by some kind of filter. But I am not familiar with any ...
3
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2answers
154 views

Auto-correlation function, an inverse problem

$x[n]$ is a complex function $n=0,1,2,\cdots,L-1 $ we assume $x[n]$ is periodic in its index: $x[n+L]=x[n]$ Its auto-correlation function $C[n]$ is uniquely defined as: $$ C[n]=\sum_{i=0}^{L-1} x[i+...
2
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2answers
124 views

Why use $\chi^2$ test to determine the presence of white noise?

I want to test for the presence of broadband noise in a snapshot 1000 complex baseband samples recorded by a software defined radio. As a follow-up to this post, why was the $\chi^2$ test used? How ...
2
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1answer
2k views

Effect of Windowing Function on Autocorrelation Function

I need to compute FFT components and autocorrelation of a discrete signal. When I do not use any window function before taking FFT of the signal I get a reasonable AC function from FFT that includes ...
2
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5answers
9k views

Where does the delta function come from if we derive autocorrelation directly?

I am reading a book "Creating Noise" written by Hollos & Hollos and have a question about the autocorrelation function of the Gaussain white noise when reading the following passage: From the ...
2
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1answer
268 views

Decorrelating Stationary Colored Gaussian Noise — Effect On The Desired Signal

So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$. In ...
2
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2answers
4k views

Cross-correlation peak

How get cross-correlation peak and based on it calculate correlation score for similarity of two audio samples. SO far I've FFT two samples complex conjugate second multiply results IFFT cross-...
2
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1answer
48 views

the demonstration that states that the FT of the ACF function is the square of the DTFT of the signal

I am following the book The Intuitive Guide to Fourier Analysis & Spectral Estimation with MATLAB. I am trying to selflearn the fourier analysis in matlab. I got lost in one passage in the ...
1
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1answer
624 views

Expectation of product of Filtered White Gaussian Noise

Assume I have a random process $X(t)$ that is white gaussian noise with psd $S(f)$. Now, let's filter that noise through a LPF of bandwidth $B$. How would I evaluate the following expression: $$E[S(...
1
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1answer
2k views

What is the unit of autocorrelation function?

In general, for autocorrelation of the deterministic signals,from the formula what is the unit of it.
1
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1answer
419 views

How to choose a phase for the deconvolution of an autocorrelation?

Say I have a function, $C=C\left(x\right)$, whose fourier transform is denoted by $c=c\left(k\right)$, i.e. $C\left(x\right)=\sum_{k=-\infty}^{\infty}c\left(k\right)\chi\left(x\right)$, where $\chi\...
1
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1answer
635 views

Division by zero in Levinson–Durbin recursion?

I am doing a LPC analysis of a speech signal using the autocorrelation method. To calculate the LPCs I am using the Levinson–Durbin recursion. In my literature the error is initialized with the first ...
1
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1answer
230 views

Should I observe a signal multiple times for MUSIC algorithm?

In a paper Multiple emitter location and signal parameter estimation, the well-known MUSIC algorithm starts by calculating covariance (autocorrelation, whatever) matrix with: where overlines stand ...
1
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2answers
504 views

Does the auto-correlation function of stationary random process always converge?

The auto-correlation function of the stationary random process only depends on the time difference $\tau$. http://web.ntpu.edu.tw/~yshan/chapter6_han.pdf 64th slide of this lecture note mentions ...
0
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0answers
38 views

Interpreting Auto correlation results

I used xcorr function in Matlab to compute the autocorrelation of my signal. I obtained a graph, which is shown below. How to interpret this? I read that autocorrelation helps in finding the patterns ...
0
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1answer
100 views

How do we compute distrubtions of the value of a random process conditional on initial conditions?

Suppose I have a stationary process $\phi(t)$ with a known autocorrelation function $$ A(\tau) \equiv \langle \phi(0) \phi(\tau) \rangle$$ and suppose I also know that $\phi(t)$ is Gaussian ...
0
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1answer
140 views

Estimating confidence intervals for the mean value

Say I conducted a numerical experiment -a time-dependent fluid simulation- and extracted a time-series of some variable. It looks like this: As a result of the simulation, I am supposed to report the ...
0
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1answer
3k views

How to find the period of a noisy signal using MATLAB's $\tt xcorr$?

Here is my code: function [ T ] = FindPeriodicity2(x,Fs) ac=xcorr(x,x); [~,locs]=findpeaks(ac); T=mean(diff(locs)/Fs); end and when I pass the signal ...
0
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1answer
235 views

What is the significance of a spike like autocorrelation function

I have some questions and doubts to which the answers are difficult to extract from text books. Hence I have posted this question here. Help would be extremely beneficial. Thank you. (1) The ...