Questions tagged [autocorrelation]

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

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How to calculate auto-correlation of a bpsk modulated signal or how to calculate expectation value of complex exponential function

How to calculate auto-correlation of a bpsk modulated signal, or how to calculate expectation value of complex exponential function manually not by using matlab or any other software? For example, if ...
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1answer
331 views

Find the time lag for a wave

suppose that we have a wave which has some peaks in some indexes like 2,12,25,... and otherwise zero. I want to extract the time lag or lags between peaks of a signal. could anyone help me ?
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3answers
2k views

How to get fundamental frequency of a signal using autocorrelation?

I am trying to get the fundamental frequency of a signal that only has a single pitch. I coded out the autocorrelation function using FFT and already got the autocorrelation result. Unfortunately, I ...
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0answers
294 views

Proving a cyclostationary processes signal

Suppose a random signal $x(t)=\sum\limits_{n=-\infty}^\infty Z_n \delta(t-n\tau)$, where $ z_n = Z$ and $Z$ is a random variable with equal probability to be $+-1$, is passing through a low pass ...
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2answers
584 views

Autocorrelation Jitter

I'm doing autocorrelation (via fft) on pure, synthetic generated sinusoids and getting unexpected jitter in the results. The jitter depend on where in the sine the signal buffer is started. I get ...
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1answer
473 views

Assumptions for Hurst exponent calculation

Are there any general assumptions for the calculation of the Hurst exponent? Does the signal need to be stationary, for example? Does it depend on the method? What about the length of the time ...
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3answers
10k views

Why does the autocorrelation get its peak at zero?

I know that zero shifting in the autocorrelation function is equal to its energy, yet, I would like to understand why the peak is at zero.
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2answers
1k views

How identify echo patterns in audio samples

How do I estimate if in recorded sound samples is present an echo caused from walls reflection ? (maybe there are multiples echoes: delayed, attenuated versions of the signal itself). I'm recording ...
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1answer
1k views

Generating good synchronization sequences

As part of my work I am putting together a simple bursty BPSK communication system. I want to make the demodulation easy, so I am going to put a synchronization sequence at the beginning of each ...
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1answer
165 views

When might looking at rising edges perform better than cross-correlation?

A simple question as the title indicates: Let us assume that we have two signals, measured from two different sensors that are close together. (For this application, the sensors are measuring blood/...
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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 ...
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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 ...
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4answers
43k 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 ...
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1answer
363 views

Designing a feature vector for discriminating between different sonic waveforms

Consider the 4 following waveform signals: ...
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4answers
8k 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 ...
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1answer
1k views

On using eigenvectors to estimate a signals' fundamental frequency, via MUSIC

Context: (Disclaimer: This is NOT a comm problem). I am trying to estimate the fundamental frequency of a real, periodic signal. This signal, was constructed by match filtering a raw signal, to that ...
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2answers
1k views

Best way to evaluate “quality” of autocorrelation?

This is a side-trip from my snoring app. I had a crack at producing an autocorrelation of the audio signal, to see if that "correlates" with snoring/breathing very well. I have a simple algorithm ...
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1answer
1k views

What Does Make an Error Surface Convex? Is It Determined by the Covarinace Matrix or the Hessian?

I am currently learning about least-squares (and other) estimations for regression, and from what I am also reading in some adaptive algorithm literatures, often times the phrase "... and since the ...
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2answers
1k views

signal uncorrelated with delta in the origin

I have a stochastic process completely uncorrelated. Why the autocorrelation function has a delta of dirac in the origin? Which is the reason of that? $R_{XX}({\tau})=A{\delta(\tau)}$ where $R_{XX}$ ...
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3answers
433 views

Extraction of non-sinusiodal repetition rates

I have an auto-correlation function that was generated from a signal, and I am trying to extract its 'repetition rate' in order to calculate the dominant frequency of the pulse, but I am not exactly ...
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2answers
2k views

Why do we deal with the eigenvectors of the autocorrelation instead of the data itself?

How intuitively to understand why eigenvectors of the autocorrelation matrix are used, but eigenvectors of the matrix constructed from temporal samples have no sense and aren't used? For example, in ...
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4answers
2k views

Auto correlation correspondence to original time domain window

I'm trying to figure out how exactly an auto correlation corresponds to a time domain signal. Now I'm trying to find pitch periods in an audio file and 99% of the time I'm getting it spot on. ...
12
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4answers
19k 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, ...
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1answer
550 views

Relaxation time in a stationary stochastic process

Foreword: I'll give some background here because I'm not sure all my premises are correct. I encourage you to IGNORE THE BACKGROUND, unless you're really interested / bored :) The Question I want to ...
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1answer
238 views

Unit Problem in Designing a Filter for a Given Auto Correlation Function

Given a WSS process with the following Auto Correlation Function: $$ r\left ( \tau \right ) = {\sigma}^{2} {e}^{-\alpha \left | \tau \right |} $$ The Laplace Transform would be: $$ R \left ( s \...
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4answers
13k 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 ...
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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?
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3answers
20k views

Autocorrelation in audio analysis

I'm reading up on Autocorrelation, but I'm not sure I understand exactly how it works and what output I should expect. Am I right in thinking that I should input my signal to the AC function and have ...