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

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Autocorrelation of white noise

Autocorrelation of white noise should have a strong peak at '0' and absolutely zero for all other $\tau according to this. Then why is output of this code a cone shape(with the expected 'strong peak' ...
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53 views

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 ...
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19 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 & ...
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39 views

Reliable peak picking algorithm?

I've written an application that estimates pitch based on autocorrelation function. I did peak picking by comparing vector values to determine whether the central one is a peak or not, but this method ...
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76 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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25 views

Random jump process between {-1,1} with time delay [closed]

I want to calculate the autocorrelation function $R_{xx}$ of the signal $X\in\{-1,1\}$ that jumps with probability p between the two values: \begin{equation*}X_{k+1} = \begin{cases} X_k &1-p \\ ...
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48 views

How to get the melody from a signal

I'm trying to retrieve a melody from a signal (simple sine with 3 notes). I've windowed the signal and performed autocorrelation to get the fundamental frequency of each window and then converted ...
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36 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 ...
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1answer
56 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, $x(t)$ ...
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99 views

Autocorrelation of a telegraph process/constant signal

I am trying to calculate the autocorrelation function for the telegraph process, but I somehow don't get the right results. I am calculating the correlation function of a signal X which can take ...
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1answer
41 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: ...
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35 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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59 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 I ...
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65 views

Autocorrelation Function and Power Spectrum

My aim is to determine the power spectrum of a signal of finite duration using Its autocorrelation function Performing FFT directly on the time-domain data The function is defined as follows in ...
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105 views

Correlation using FFT/IFFT (fast convolution) in Java - not centered

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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49 views

Convolution sum vs auto-correlation problem

I had an exam one of these days and one of the questions was: "Knowing that an auto-correlation estimator of a sinal x[n] could be defined by: $$ R_{xx}[k] = \sum_{n=-\infty}^{+\infty}h[n].x[n+k] , ...
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201 views

How to find peaks and periods?

I am looking at data like this: Source data: http://pastebin.com/raw.php?i=L6cd8d5K The data is quasi-periodic, there is a distinct cycle but it is not an exact repeat, and the period changes ...
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64 views

Determining the uncertainty of an autocorrelation

My problem should probably be built up from the beginning, so lets start there. I performed a certain experiment 25 times. Every time, the experiment consists of 5000 measurements, and each ...
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1answer
55 views

Autocorrelation function of a discrete signal

For a certain experiment of which I have data, I want to calculate the autocorrelation of the measurements. For this I used the expression from http://en.wikipedia.org/wiki/Autocorrelation#Estimation, ...
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20 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 ...
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2answers
198 views

Algorithms for finding fundamental frequency based on ACF result

I am developing a software for fundamental frequency tracking. For this purpose, I have designed a function which calculates autocorrelation over the signal and a second function which, based on ...
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1answer
71 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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24 views

DPD auto and crosscorrelation [closed]

I am trying to learn signal processing and digital pre-distortion. http://www.altera.com/end-markets/wireless/advanced-dsp/predistortion/wir-digital-predistortion.html I am currently trying to auto ...
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23 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 ...
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152 views

Matching two audio inputs (signals) [duplicate]

this is for an application in which passwords are stored in the form of audio inputs . In order to provide user access , the password(in audio form) will be matched with already stored password(audio ...
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47 views

Using Spectral Density To Compute The Autocorrelation Function

I have a spectral density function $S_{xx}$ and I want to compute the discrete autocorrelation function $r_{xx}[n]$ from it but I can seem to figure out how.I have $$ S_{xx} = 3e^{-2jw} + ...
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153 views

Applications of Correlation in Signal Processing

There have been discussions on the differences between convolution and correlation, autocorrelation, cross-correlation, et al. In spite of looking at the visualizations, and understanding the ...
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1answer
92 views

How to derive a rate (e.g. water dripping) from an audio file

I want to learn how to go about analyzing some audio files I have acquired. Let's say the files contain some sort of repeating sound (e.g., water dripping), and I want to derive the pattern of the ...
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213 views

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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269 views

Choosing Codes or sequences with excellent Auto-Correlation properties

The Auto-Correlation function of Walsh-Hadamard codewords does not have a good characteristics. It can have more than one peak and thus, the Walsh-Hadamard codes do not have the best spreading ...
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86 views

How do we know that CTFT of the autocorrelation function is the PSD?

I know that the Fourier Transform of the autocorrelation function is the Power Spectral Density. But how can we arrive at such a result intuitively? Is it just a theorem?
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266 views

If an autocorrelation function of a process is a rectangular function, then is the process deterministic?

I would like to clarify one doubt regarding autocorrelation function $R_x (\tau)$ of a process $X(t)$. Suppose $R_x (\tau) = \Pi (\tau)$, where $\Pi (\tau)$ is the rectangular function. Then is the ...
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94 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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44 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 ...
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1answer
45 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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70 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 ...
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177 views

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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123 views

Autocorrelation of a stochastic process which is a sum

Let's say that a stochastic process is defined as $$X(t) = \sum_{n = -\infty}^{+\infty} X_n * f(t- nT)$$ where $X_n$ is the $n$-th symbol among independent random symbols. I have proved that ...
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102 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 ...
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1answer
351 views

Autocorrelation - Stochastic vs deterministic processes

On one hand, there is the statistical definition: $R_x(\tau) = \frac{\operatorname{E}[(X_t - \mu)(X_{t+\tau} - \mu)]}{\sigma^2}$ and on the other hand, there is this other definition (e.g. see ...
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1answer
159 views

Speech discrimination from animal sound

i am looking for discrimination of speech from animal sound if you take a 150ms frame of speech and bird as shown below, what feature can i extract from them so that i can effectively state the ...
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1answer
619 views

AutoCorrelation using FFT of power spectrum

I have a chunk of data (samples) that need to do autocorrelation using FFT method. All data are real and lies between -1 and +1. What I have done follows: Zero pad the window with the length equals ...
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184 views

Fourier transform of Autocorrelation function, what am I missing here? (Power spectrum)

Given this problem I know that the autcorrelation and power spectrum are fourier pairs, so when taking taking fourier transform of Rxx, one should end up with Sxx However, when I take the ...
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1answer
151 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 ...
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2answers
89 views

Simplification of a convolution-like expression

I am trying to further reduce the following expression (if there's a nicer way to write it): $\sum_{k=-\infty}^{+\infty}\sum_{p=-\infty}^{+\infty} \sum_{l=-\infty}^{+\infty} w(k) ...
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96 views

What happens to signal, if we offset periodic auto-correlation?

suppose $x_n$ is an $N$-point sequence with periodic auto-correlation $$ c_n=\sum_m x_m x_{(n+m) mod N} $$ How to find $N$-point sequence $y_n$ with periodic auto-correlation $d_n = c_n - A$, where ...
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63 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 ...
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1answer
38 views

What data should be collected to determine the autocorrelation sequence?

For a current project I need to implement an algorithm that needs the autocorrelation sequence of the channel, as part of a key step. We're measuring the frequency utilisation in our local area - ...
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1answer
67 views

Measure of harmonicity in a time-series

I'm analyzing speech signal for identifying voiced and unvoiced regions. Voiced regions are supposed to have a "pitch", which can be estimated using auto-correlation function (ACF). Basically, one ...
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49 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 ...