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

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Concepts Surrounding First Two Samples in Difference Equation

I'm attempting to construct a difference equation in matlab for the function u(n) and find the auto-correlation matrix R. I'm following the technique as is defined by my text below: The system I'm ...
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21 views

Length and spacing autocorrelation with FFT

I have calculated, with FFT and A-FFT, the autocorrelation of a discrete signal (coming from an integration) with spacing $\Delta T$ composed by $N$ samples padded to $2N$ with zeroes. What is the ...
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66 views

Determining Power Spectral Density from Autocorrelation Function and Time-Series Data

So I think I've confused myself a bit here. I know that taking the FFT of time-series data (wind velocities, for example) yields a power spectral density. However, I just read that taking the Fourier ...
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22 views

what kind of information we can get if the auto-correlation for an image is a ring or two rings?

I did the auto-correlation for an image by Mathematica. The auto-correlation function shows rings as follow..I am sorry that I can not attach the original image here. From the following ...
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13 views

Deconvolving two vectors produces a single number (not a vector)

I am trying to deconvolve the auto-correlation of my source wavelet (Ricker wavelet) from my receivers responses. Now if I deconvolve the source wavelet out of the response I get a vector back and the ...
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38 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 ...
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57 views

why is the plot of the PSD of this autocorrelation function oscillating?

I was doing an exercise trying to compute the PSD of the following discrete autocorrelation function: \begin{equation} r_x(m) =(1/2)^{|m|} \end{equation} In this simple matlab code that I came up ...
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43 views

Detecting an echo using the autocorrelation of the cepstrum

I'm trying to implement an echo hiding steganography technique. I need a way to detect an echo in a audio segment. The documents I've been looking mention that I need to do an "autocorrelation of the ...
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84 views

Efficient calculation of correlation function every N_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 ...
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33 views

Video: Detecting a digital timer and when it ticks

Input: A video with a digital timer, possibly several hours long, such as this video. The timer might use any font or color, and might be located anywhere on the video, but it probably won't fill the ...
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34 views

regarding autocorrelation and derivation of original signal

$$r_x(t)=\begin{cases} 2-2t ,& 0 \le t \le 1\\ 2+2t ,& -1 \le t \le 0 \end{cases}$$ So how do I get original $x(t)$ from this? I tried integrating the equations, and the value I got was ...
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78 views

Least squares and auto and cross correlation

I am trying to understand why auto and cross correlation helps find the best fit line in least squares. I have an equation as stated here: $Ax=b$ -- I have not exact solution, so I use the least ...
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35 views

Ambiguity function of multiple sines

I was reading through the Ambiguity function, and I was wondering if it's possible to calculate analytically (or numerically) the ambiguity function of a sum of sine waves. In case of a single sine ...
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1answer
87 views

autocorrelation A to K conversion for LPC speech analysis?

I am building an LPC analysis tool for speech synthesis and did the following to generate my a0 through a10: ...
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1answer
45 views

Auto/cross correlation of a cosine in the context of an adaptive beamformer

I am currently reading chapter 13 of 'Adaptive Signal Processing' by Widrow and Stearns, so if anyone happens to have a copy of the book to hand it could be helpful. I am reading the chapter on ...
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119 views

Improving an auto-correlation based guitar pitch detector

I've seen many questions on this forum regarding pitch detection for musical instruments (commonly guitar), and spent a while reading through the answers to create a basic implementation of ...
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1answer
157 views

Uses of peaks in audio auto-correlation

Do you know of any algorithms for audio processing that make use of peaks in auto-correlation function? I am currently involved in research on mapping methodology for dynamic algorithms. I came ...
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130 views

Problem in Implementing Cyclostationary Feature Detector in Matlab

I have Implemented this detector in AWGN channel in Matlab but I am getting vague result. As it performance doesn't vary with change in SNR. Its very strange result for me. I don't know what mistake I ...
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61 views

Conceptual queston on Z transforms and time series model (Part1)

I am few questions from the following papers: ...
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27 views

Calculating energy spectral density?

For surface of self-windowed function $x_x[n,k] = x[n]x[n-k].$ I can think to make two fourier transforms, one over $n$, and one over $k$. Question: Can anyone highlight an interpretation of each? ...
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10 views

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

Suppose I have a 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 distributed. If I ...
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57 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. $ ...
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118 views

A filter in IOS to eliminate a certain frequency range

I am making an application where I record sound on an IOS device using the built-in microphone. I want to process the sound in such a way that only frequencies in the 16-18 kHz range remain; the other ...
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72 views

Is speech stationary ? How do I test it in matlab?

I'm taking a "Random Signals" class in school and I've got an simple assignment about speech in matlab. I have been asked to record two files: A single word or sentence. A couple of syllables each ...
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64 views

Get a power spectral density from real random data

I am using real data of wind, which is a random one to get the power spectral density of these values. How can I do to get this PSD in matlab, and Can I get an analytical expression for this psd. ...
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29 views

Issue in partial correlation

For a time series I wanted to plot separately the partial auto correlation. Below is the graph for MA model that I want: This shows plot of two time series of two time series - one is a sequence ...
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175 views

Autocorrelation and FFT : avoid zero-padding

Some posts evocate the computation of convolution or cross-correlation using FFT and zero-padding the temporal signal. I want to compute the autocorrelation of a 3D array using FFTW (2 dimensions are ...
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115 views

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 ...
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1answer
110 views

Kalman Filter Estimate vs ACF Least Squares Estimate

I am currently reading Chapter 5, Applications to the Gas Markets, in Stochastic Modelling of Electricity and Related Markets by Benth, Benth and Koekebakker, World Scientific, 2008. In the ...
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76 views

Equivalence of FFT and PSD based output based on the Frequency Response Function

Correct me please if I am wrong... I have just started working in the domain of signal processing using the Fourier Transform ($\mathbf{FFT}$) and Power Spectral Density ($\mathbf{PSD}$). I am trying ...
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1answer
66 views

Autocorrelation of a signal comprised of only the same number

In MATLAB I generated a signal and its autocorrealtion function using: signal = ones(1,500).*5; % a vector of the number 5 acf = autocorr(signal,numel(signal)-1)); To my suprise the ...
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131 views

Cross-Correlation : Comparing two signals or finding the location of a target

I read across places that cross-correlation of two signal (a radar sending a signal and receiving it back) one can detect the location (distance) of a target from a point and that cross-correlation ...
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132 views

Correlation : Cross correlation why we need to multiply the samples

I understand what books states about cross-correlation of signals and their mathematical representation: For continuous functions f and g, the cross-correlation is defined as: $(f \star g)(\tau)\ ...
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130 views

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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61 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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29 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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108 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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92 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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32 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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1answer
63 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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66 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
146 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, $x(t)$ ...
4
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1answer
400 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
97 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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57 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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165 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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162 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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1answer
553 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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1answer
150 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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2answers
314 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 ...