# Questions tagged [autocorrelation]

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

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### Efficient calculation of correlation function every $N^{\rm th}$ point

I would like to calculate a long correlation function of length say, 1e6 points. I have a prior knowledge that the correlation peak will be in point k*1000. Is there an efficient way to apply this ...
369 views

### 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 ...
1k views

### 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 ...
3k views

### 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 ...
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 ...
886 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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### 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($\tau$)=...
223 views

My question is a mix of signal processing and Matlab coding. I have an FIR filter with added noise $w_n$ $$x_n=\sum_{m=0}^{N_h-1}h_mg_{n-m}+w_n.$$ Now the noise $w_n$ has the autocorrelation $$E[... 0answers 94 views ### Zero-padding vs. nonzero-padding in computation of auto-correlation with FFT Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal? If I have a measured signal which has good ... 0answers 54 views ### How to deduce the shape of autocorrelation graphically? I'm asking for your help in understanding if I have a rectangular function, so the autocorrelation for it will be triangular... and I can prove that graphically but this is time-consuming especially ... 0answers 36 views ### E(X(t)X(t))=\sigma^2\delta(\tau) or E(X(t)X(t))=\sigma^2 (Question already asked on Math StackExchange) Let's say we have a white noise process x(t) such that: E(X(t)X(t+\tau))=N\delta(\tau) E(X(t))=0 In particular, with \tau=0, E(X(t)X(t))=E(X^... 1answer 427 views ### Confusion about PSD and RMS Let's say I have a noise power-spectral-density (PSD) which is not flat and ranges from 0 to f_1 Hz in frequency. As we know, the total area under the PSD is equal to the total average power of the ... 2answers 87 views ### Image Interpolation Using the Yule Walker Equations I have been studying about the Yule-Walker equations for prediction of a time series data from knowledge of past values of the series. Is there any way I can use the same in an image to exploit the ... 0answers 107 views ### Subtracting audio signal emitted - trying to use spectral subtraction to localize moving objects I am a Software Engineer without much signal processing background and currently spending and experimenting to get use to it. My scenario: Assume a speaker and a microphone array. A speaker emits an ... 0answers 345 views ### Power Spectral Density of a WSS Random Process with 2D Discrete Fourier Transform I'm trying to understand how the random process (RP) signal in discrete time domain is related to its power spectral density (PSD) in frequency domain if the signal is wide sense stationary (WSS). If ... 0answers 78 views ### derive AR model based on the autocorrelation of jakes model I am trying to derive the channel model based on the autocorrelation of Jakes model. In step 2, i am trying to get rid of s(n+1) by inserting it to s(n-k) in which the limit will change. However i ... 0answers 308 views ### Event detection in a running person's acceleration data I am trying to detect some events on this signal : This is the acceleration of someone running. By eyes we can detect many blocs, sometimes separated by a little interval. I would like to be able to ... 0answers 73 views ### Autocorrelation of a L-point moving average system The L-point moving system is:$$y[n]=\frac 1L\sum_{k=0}^{L-1}x[n-k]$$x[n] is a Bernoulli random signal with \beta=0.5 (equal probability) The autocorrelation of x[n]: \psi_{xx}[m]=\delta[... 0answers 23 views ### Power Spectral Density Via Rank 1 Update I know that I can find the autocorrelation matrix of a series of finite length sequences via rank-1 updates using the relation: \mathbf{R}[k] = \frac{1}{k}\mathbf{R}[k-1] + \frac{1}{k+1}\mathbf{r}[k]... 0answers 192 views ### Construct a correlation matrix using the covariance method I want to compute the autocorrelation matrix by using the covarience method. X(n) is the harmonic process X(n) = \sum\limits_{i=1}^3 A_i e^{jn\omega_i} + V(n) V(n) is unit variance noise.  ... 0answers 145 views ### The autocorrelation of a WSS process as a linear operator If I'm given a autocorrelation matrix of a WSS process what interpretation should I put on the resulting vector. More concretely the matrix takes the form \begin{bmatrix} x_1 & x_2 & \... 0answers 369 views ### Noisy Signal auto/cross-correlation I am trying to understand the basics of the cross/auto-correlation if the noisy signal y(t) which is received from the channel at the receiver. Here at receiver we want to estimate the noise in the ... 0answers 266 views ### ACF and PACF Confidence Levels for ARMA I'm trying to figure out where exactly to draw the confidence levels for the autocorrleation function (ACF) and the partial autocorrelation function (PACF) for an ARMA model. For PACF I found that a ... 0answers 58 views ### peak-to-peak test between two signal Suppose that we have different signals (Pulses). I would like to study which signal has deterministic peak-to-peak distant (lag). For example A=[1 0 0 1 0 0 0 1 0 0 1] and B=[1 0 0 1 0 0 1 0 0 1] and ... 0answers 277 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 ... 0answers 194 views ### Random signal modeling with Matlab I want to build a detector of sorts. Say I have a bunch of signals and they all share some patterns, like some peaks in frequency or something more complicated that I can't bother to calculate by hand.... 0answers 653 views ### What is the best pitch (frequency detector) for a Voice Activity Detection Algorithim? I am programming a Voice Activity Detection algorithm. After researching several methods, I implemented a simple method that determines whether or not the person is speaking based off the RMS of the ... 0answers 202 views ### Evaluating auto correlation strength (Gamma) I'm working on Cognitive Radio in TV Band Spectrum. I need to sense the presence of signal in a particular spectrum. I have to sample the incoming signal (say 1000 samples) and I have to find the ... 0answers 300 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 ... 1answer 1k views ### Obtaining power spectrum from ACF, FFT using Matlab and FFTW I am using Matlab R2012b 64-bit on Windows 7 in order to estimate the power spectrum of a simple signal that is:$$\cos(10t) + \sin(20t) $$defined in the time interval from 0.0 to 10.0 Here is what ... 0answers 30 views ### Why are the Fourier transforms of autocorrelation and cross-correlation different? I'm almost definitely misunderstanding this, but as far as I can tell we can equate the Fourier transform of the auto-correlation function R_{xx}(\tau) with power spectral density (PSD) like so: \... 0answers 25 views ### Get autocorrelation function from the power-spectrum (python) I am trying to compute the autocorrelation function of a signal for which I only know the power-spectrum. In order to test my approach I wanted to try it out on the spectrum of 1/f^2 noise for ... 0answers 23 views ### Stereo echo cancellation for stationary source locations: why does adaption stagnate? In a stereo echo cancellation system, the echo path for the far-end-signal in the near-end room is estimated by an adaptive filter. Since the same signal is transmitted by two similar far-end paths, ... 0answers 18 views ### Power spectral density of surface roughness I am currently working on understanding how visually and intuitively the power spectral density is the fourier transform of the autocorrelation of a signal. I was wondering if anyone had a good ... 1answer 36 views ### estimation of ARMA(1,1) with MA parameter greater than 1 I am working with the following simple ARMA(1,1) model:$$ z_{t+1} = \phi z_{t} + \theta\varepsilon_{t} + \varepsilon_{t+1}  In my case $\theta$ depends on some other parameters, and, therefore, I ...
When computing the energy of a NON-STATIONARY (transient) random discrete-time signal $x(n)$, does it make more sense to compute the energy as $E=\sum_1^N{x^2(n)}$ over all the $N$ samples or does ...