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

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Variance of estimating coefficients by correlating a sequence

I have a sequence $$ r[n] = a_1.t_1[n] + a_2.t_2[n] + a_3.t_3[n] + ... $$ where $t_1, t_2, t_3,...$ are uncorrelated, two-level (+A/-A), zero mean, pseudo-random sequences. To estimate $a_1$, ...
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28 views

Extracting direction of dominant sinusoids from an image in terms of angles

Here is a sample image. What I am looking to do is compute the dominant "wrinkle" directions. The dominant wrinkle directions can be seen in the following FFT, roughly, by drawing a line through ...
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1answer
43 views

Power Spectrum Analysis

In order to find a peak or max response in the fourier domain as in the spatial domain, I have been studying bartlett's method, welch's method, and the blackman-tukey method for more accurate power ...
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1answer
48 views

Autocorrelation for the sum of a deterministic and stochastic signal

so I'm working on a problem where I need to find a PSD for the sum of a deterministic and stochastic function. So assume $x(t)$ being this sum: $x(t) = d(t)+s(t)$ where $d(t)$ is the deterministic ...
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32 views

What is the unit of autocorrelation function?

In general, for autocorrelation of the deterministic signals,from the formula what is the unit of it.
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56 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 ...
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1answer
44 views

Division by zero in Levinson–Durbin recursion?

I am doing a LPC analysis of a speech signal using the autocorrelation method. To calculate the LPCs I am using the Levinson–Durbin recursion. In my literature the error is initialized with the first ...
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24 views

Detecting two changing inharmonic pitches

I have a recording of a newer type of siren that uses two pitches sliding back and forth in time. I want to be able to detect both of the pitches simultaneously or overlapping at short intervals. ...
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1answer
40 views

Linear Prediction Coefficients

I want to learn how to compute linear coefficient, but to be honest - I can't. I know how to use them if i have it and why I want them. Suppose this toy example: A signal $x=[-1, -2, 0, 1]$ ...
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1answer
41 views

How to get the autocorrelation of this finite discrete function?

This is the function: $$ x(n) = \begin{cases} 1, & \text{-N $\leq$ n $\leq$ N ;}\\ 0, & \text{otherwise.} \end{cases} $$ And I tried to solve it, using sigma notation or summation: ...
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1answer
63 views

PSS convertion from Frequency to time domain

Hi I have a question regarding primary sync signal in LTE. It is generated in frequency domain and its length is 63. How to convert this signals frim frequency to time domain. Should I use IFFT? what ...
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51 views

Autocorrelation Lag In Seconds Explanation?

I am using a MatLab audio feature extraction toolbox (MIRToolbox), and I am in the process of cross correlating an onset curve (envelope). I am aware of what the lag means when using Matlab's ...
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11 views

How modulation spectrum of zebra finch song is calculated

I read this advanced signal processing technique in Neuroscience Journel. Modulation spectrum is a spectral modulation vs temporal modulation plot. Please tell procedure of plotting it step by step. ...
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20 views

Frame-level autocorrelation coefficients with lags bigger than frame size

I am reading the paper "Automatic Generation of Social Tags for Music Recommendation" and struggling with understanding this: The features we use include [...] 176 autocorrelation coefficients ...
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1answer
17 views

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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35 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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1answer
147 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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25 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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17 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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1answer
72 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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1answer
121 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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84 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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1answer
124 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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1answer
52 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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37 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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1answer
110 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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1answer
73 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
124 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
54 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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1answer
272 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
173 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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175 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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68 views

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

I am few questions from the following papers: ...
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28 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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1answer
52 views

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

Suppose I have a stationary 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 ...
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64 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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177 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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92 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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83 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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236 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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1answer
225 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
158 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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89 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
72 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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1answer
192 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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1answer
193 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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1answer
162 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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1answer
71 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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34 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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131 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 ...