Questions tagged [autocorrelation]

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

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What is the autocorrelation equivalent of the spectrogram called?

I'm very knowledgeable about the differences between the Fourier transform, and the autocorrelation; mainly that one converts the time domain to the frequency domain, and the other finds periodicities ...
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Advice on autocorrelation via FFT

I have been creating an application in Java that transforms an audio signal and writes it to a midi file. At first I tried using autocorrelation to find the fundamental frequency. However, I have ...
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Correlation Using FFT / IFFT (Convolution in Frequency Domain) in Java

I try to find about the delay between two audio files using Cross Correlation in Java. I've already done this algorithm so far that i get a idea about how many samples is the delay. FFT x1 -> Zero ...
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338 views

Remove the extra peaks by lag

Suppose that we have some peaks of a signal and we know the time lag between dominant peaks. How is it possible to remove the extra peaks by applying time lag ? Lets say it in MATLAB ...
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1answer
809 views

Calculation of an autocorrelation function

A sample of a random process is given as: $$ x(t) = A\cos(2\pi f_0t) + Bw(t) $$ where $w(t)$ is a white noise process with $0$ mean and a power spectral density of $\frac{N_0}{2}$, and $f_0$, $A$ ...
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How to construct Polyphase (Frank) codes in MATLAB

I have written a piece of code in MATLAB to generate Frank codes - Pastebin link for pulse compression. I know that Frank codes are stepped frequency approximations to Linear Frequency modulation(LFM)...
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3answers
207 views

How can define an indicator which measures the degree of similarity between two signals?

The similarity of two signals is calculated by cross correlation. But, how to define an indicator which quantitatively measures the degree of similarity between two signals? Thanks.
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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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1answer
120 views

Correlation of independent random processes

Suppose $X(t)$ and $Y(t)$ be two independent random processes. Is $E(X(t_1)Y(t_2))$ necessarily zero?
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1answer
103 views

perfect sequences

I have heard somewhere that sequences with perfect autocorrelations and crosscorrelations do not exist. I have been searching for an insight into this claim, but have not been successful. Can anyone ...
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2answers
409 views

How to compute autocorrelation of signal defined by difference equations?

I have no experience with difference equations and I want to learn how to compute the following, but I found no resource online. Any help would be greatly appreciated. Find: $$\mathbb{E}\left[d[n]d[...
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115 views

Weighted Sum of Auto Correlation - Lower Bound

Given a vector $ v $ with elements $ {\left\{ {v}_{n} \right\}}_{n = - \infty}^{\infty} $ and denoting $ {v}_{n}^{\left( k \right)} = {v}_{n - k} $, namely, a shifted vector by $ k $ elements (Mind ...
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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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160 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 ...
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2answers
2k views

Definition of average power?

There are two kind of average power I encountered in random signal class and textbook: definition 1: average power =$$E[|x(t)|^2]=R_{xx}(0)=\int^\infty_{-\infty} S_{xx}(f)\,df$$ definition 2: average ...
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How to prove that the peak of the autocorrelation function is at zero lag?

Show that for a signal $f(\tau)$ with finite energy and energy autocorrelation function $\phi^e_{ff} (\tau),$$$|\phi_{ff}^e (\tau)| \leq \phi_{ff}^e (0), \ \ \forall \tau.$$ According to my textbook ...
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Derivation of $ R_{N(t)}(\tau) $ from its $f_{N(t)}(\eta)$

How can we prove the auto-correlation function of white gaussian noise $\{ R_{N(t)}(\tau) \}$ is $\frac{N_0}{2} \delta(\tau)$ from its p.d.f in equation below? $$ f_{N(t)}(\eta)=\frac{1}{\sqrt{2 \pi \...
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1answer
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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 $X(t)$...
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Correlation meter

I have three questions regarding the correlation meters used in audio. How are they calculated? I have heard correlation is performed by convolving one signal with the time flipped version of a other,...
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1answer
64 views

What is the set of most predictable or in other words most self-correlated signals?

Which signals or set of signals is the most predictable or in other words most self-correlated (autocorrelation)? I think one of them is $x(t)=c$, for all $t$, where $c$ is a scalar constant. The ...
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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-...
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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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Understanding Pitch Detection with Autocorrelation Methods

I've been reading through A Smarter Way to Find Pitch, describing its pitch detection algorithm using autocorrelation. I've been having trouble understanding the accuracy claims. It says: MPM runs ...
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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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1answer
350 views

Linear Predictive coding vs AR modeling

I'm looking for a suitable explanation of the circumstances in which the LPC error polynomial for a discrete time process x[n] is replaceable with an error polynomial categorized under the AR model? I ...
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3answers
178 views

Interpreting this plot cross-correlation

I have an input signal $x(t)$ that is a white Gaussian random signal with mean 0 and variance 1. The signal $y(t)$ is the output of a linear filter with impulse response $$h(t) = |\operatorname{sinc}(...
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1answer
5k 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, ...
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3answers
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Calculating the fundamental frequency using Autocorrelation often gives half the expected value

I'm currently writing a mobile app which needs to analyse musical notes and find the fundamental frequency to determine the pitch. To do this I'm reading in audio data, taking an FFT, taking the auto-...
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3answers
335 views

Could there be any reason to prefer convolution-based calculation of autocorrelation?

Theoretically both of ways of calculating autocorrelation function are identical: strightforward convolution and Fourier-based method where we use FFT/iFFT in practice. And as it is well known, the ...
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2answers
406 views

What does the frequency axis of a Power Spectral Density mean?

I have never really understood what the frequency axis meant when we plot the Power Spectral Density(PSD). Does it correspond to frequency as we get after we take the Fourier Transform of a time ...
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1answer
610 views

Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
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1answer
166 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
257 views

Autocorrelation of a uniform random process

i am currently learning the basics of signal processing. As you may know the definition of the autocorrelation is different if you look at a random process or for example a deterministic signal My ...
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1answer
86 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 ...
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1answer
83 views

What kind of power spectrum implies uncorrelation in time?

I am new in signal processing field, and actually I just need some basic tools for what I am working on. I've learnt that the autocorrelation function is the inverse Fourier transform of the signal's ...
2
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1answer
76 views

Simulate time series given temporal auto-correlation functions

Given a random process $x[n] \in \mathbb{R}$ (say of length $N$) and all correlation functions such as: \begin{align} \langle x[i]\rangle\\ \langle x[i]x[j]\rangle\\ \langle x[i]x[j]x[k]\rangle\\ \...
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1answer
35 views

Why is the sound field intensity due to $K$ point sources given by $ I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)$?

I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below. Statement: 1. We ...
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1answer
110 views

Destructive interference on the Autocorrelation of the time signal of periodic CPFSK-signals.

An FSK-signal with a frequency-shift $\Delta F$, a symbol-stream $x$, $x(n) \in {\{-1,1}\} $ and symbol duration $T$ has the complex envelope: $$f[x](t)=\exp\left(2 \pi i \Delta F T \left(\sum_{l=0}^{...
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1answer
329 views

Help in interpreting the auto correlation graph

I want to check if a time series is (a) random (b) independent. For these I am using the autocorrelation (AC). Autocorrelation refers to the correlation of a time series with its own past and future ...
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1answer
491 views

Autocorrelation - cyclic vs acyclic

In terms of signal analysis (especially frequency decomposition) would it be bad to use cyclic autocorrelation (AC) instead of acyclic/linear AC? My use case: I'm trying to characterize events in a ...
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what is equal to the FT of the Autocorrelation function

I am trying to make my own demonstration in order to find what is equal to the FT of the Autocorrelation function. The autocorrelation function in some book about turbulence is defined as: r($\tau$)=...
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2answers
212 views

Autocorrelation of signal with offset

If I have a stationary signal $x(t)$ with zero mean and with an auto correlation $r_{xx}(\tau)$, then what is the auto correlation of $y(t)=x(t)+b$ ? My calculations so far: $$\begin{align} r_{yy}(\...
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Pitch detection, YIN, pYIN

So here is the "seminal" YIN paper: Cheveigne A, Kawahara H. - YIN, a fundamental frequency estimator for speech and music and the new, improved probabilistic YIN: Mauch M, Dixon S. - PYIN: A ...
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How to visualize the autocorrelation matrix and it's properties

Having a hard time wrapping my head around autocorrelation matrix as it applies to a spectral estimation problem like MUSIC or ESPRIT. If the signal vector contains a summation of sinusoids in noise, ...
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2answers
283 views

Harmonics to Noise Ratio Estimation

I'm willing to estimate the Harmonics to Noise Ratio (HNR) of a speech signal x[k] and using autocorrelation method. Theoretically, HNR is given as, $\ HNR = \frac{R_{xx}[T_0] }{R_{xx}[0]-R_{xx}[...
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1answer
312 views

Fourier Transform gives unexpected results: signal reversal and conjugation

As far as I understand the math you can reverse a real valued signal by Fourier transformation, taking the complex conjugate of the result and inverse Fourier transformation, i.e. \begin{equation} \...
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161 views

Autocorrelation of a signal with gaps

I am trying to find the analytic expression of the autocorrelation function for a signal $X(t)$ which is defined as follows. $X(t = 0) = 1$ At random times jumps to $X(t) = 0$ happen The jump ...
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Spectral Correlation Function estimation using FAM method — implementation help

I am trying to estimate the Spectral Correlation Function by the FFT Accumulation Method (FAM) in Matlab. The way I understand the FAM method is as this link (see page 6 & 7 for FAM tutorial). ...
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How are the time scales of an exponential decaying autocorrelation related to the duration of peaks?

I'm reading a biology article (full text here) that analyzed the variation of a cell parameter over time at different stimulus intensities (calcium concentration). The frequency of peaks increases at ...
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135 views

Iterative Auto and Cross Correleation Estimates

I'm looking for literature or other information that covers iteratively estimating the auto- and cross-correlation vectors and the auto-correlation matrix. Initially, I can assume the signal is wide-...