Correlation or Cross-Correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them.

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How to implement Cross Spectral Density [duplicate]

I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image. Reading wiki1,wiki2,wiki3 from wikipedia, and ...
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49 views

Why is autocorrelation used without normalization in signal processing field?

According to the wikipedia(Link), autocorrelation has two definition. In statistics, the definition of the autocorrelation between times $s$ and $t$ is like the following: $$\displaystyle R(s,t) = ...
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28 views

Eigenvalues of correlation matrix which have the form of an harmonic function [duplicate]

As a continuation to this question, I took the matrix $C_{2 \times 2}$ which is: $$C=\left[ \begin{array}{} a& ace^{-\frac{|\phi_1-\phi_2|}{2}}\\ ace^{-\frac{|\phi_1-\phi_2|}{2}} ...
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35 views

How do I calculate the eigenvalues of a covariance matrix which contains harmonic functions

I have read that $ce^{-\frac{\phi_i-\phi_j}{\rho}}$ is a harmonic function of the form $e^{-in\phi_i}$, and therefore it's eigenvalues are one of the Fourier components of $(|\phi_i-\phi_j|)$. My ...
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28 views

How does correlation work in an image?

The discrete function for correlation over 2 dimensions is $$ C(x,y) = \sum\limits_{p=1}^{x_{res}} \sum\limits_{q=1}^{y_{res}} f(p,q)h(p+x, q+y)$$ where x,y is a coordinate in the image, f is the ...
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1answer
27 views

explanation of correlation of stationary stochastic processes

I have some doubts about correlation in stationary stochastic processes. I know that the expectation of a random variable is $$E(x)=\int_{-\infty}^{+\infty} a ...
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1answer
23 views

Correlation using fft and xcorr and plot both answers (Matlab) [closed]

I am trying to calculate autocorrelation using fft and xcorr and plot the grafhic with both cases. ...
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136 views

Triple correlation in MATLAB

How can I calculate a triple correlation between 3 signals A,B,C (each has 2 million samples)? I know xcorr do it for 2 signals by FFT each signal, multiplication and iFFT back. Since xcorr cannot do ...
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1answer
63 views

Echo cancelling using autocorrelation function

I was given a problem, but I couldn't solve. I did some researches but I still didn't figure it out. Here is the problem: An audio signal $ s(t) $ is generated by a speaker reflects in a wall with ...
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2answers
62 views

How to measure the time dependent correlation of two signals

I have two signals (time series) shown in the plot below. Just by looking at the figure, we can see that the two main peaks of both signals are very closely aligned (correlated), however the red ...
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1answer
212 views

Auto Correlation vs Cross Correlation vs Convolution and their applications

I know from wikipedia that auto correlation in done on the same signal while cross correlation is done on different signals.But what does this actually imply in terms of application.I can always apply ...
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1answer
73 views

Finding Correlation response in fourier domain

Lets say I have a system that is trying to find a small image (assume all images are grayscale) within in an image by using correlation. So this system has the baseline image, and I input 5 different ...
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2answers
79 views

PSD and $\lim_{T\rightarrow \infty} \frac 1 {2T} \int_{-T}^T x(t)\bar y(t)\,dt$

From Wikipedia, I taken a definition of power spectral density: For continued signals that describe, for example, stationary physical processes, it makes more sense to define a power spectral ...
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1answer
70 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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0answers
28 views

Correlation of an image in the Fourier Domain

I have been reading up on correlation in the frequency domain, and I just had two questions which I could not find in the book I was reading nor online: [1] So correlation is the same as a normalized ...
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29 views

Comparision between the shapes of two waveforms using coherency / correlation

I am trying to compare the shapes of two switching waveforms ... and I woud like to check whether they have the same peaks, rise times and shape... Is it possible to compare how similar they are ...
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1answer
34 views

how to find the dependence between two sparse signals?

Hi and thank you for your help. I am new to signal processing and would really appreciate your help. happy to provide more context/details. In my research, I have a system that has many sensors ...
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122 views

Correlation between two graphs in Matlab

I am trying to make a system that detects footsteps. First I filter and decimate the original signal, then I make a convolution between the filtered signal and a single footstep, then I extract the ...
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1answer
39 views

Can we decompose a correlated random variable into correlated plus uncorrelated?

Assume a random sequence $ Y_k = X_k \cdot H_k + W_k $ where $X_k$ is a deterministic quantity, $H_k$ is a correlated random sequence, $W_k$ is Additive White Gaussian random sequence. Can we ...
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5answers
122 views

Looking for an algorithm that computes “Similarity” between two signals

I'm new in this forum! ... and I'm not an expert in signal processing! ... So I hope to find help here:-) I was wondering if someone could point me to an algorithm/technique that is used to compare ...
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27 views

strange occasional periodic pattern in phase correlation output

I am working on a pattern recognition algorithm where a template is to be searched in a query image (Standard phase correlation stuff). However, in my correlation output I get some strange periodic ...
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2answers
68 views

Extract amplitudes

I have two mixed signals like $A_1f(t) + A_2g(t)$, where $f(t)$ and $g(t)$ are sinusoidal. I want to extract the amplitude infos. Directly I can not get the amplitudes (or I don't know how to). What I ...
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48 views

What is spatial correlation?

What does the spatial correlation of a signal say about it?How is it different from autocorrelation? `
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42 views

Difficulties with derivative of convolutions in Fourier domain

I am trying to solve a minimization problem in the DFT domain. I have a formula where both dot products and convolutions are involved. Capital letters are the DFT of 2d images, the overline denotes ...
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36 views

Measuring typical seperation between patches using 2D Fourier Transform

I need to extract information about the typical distance between the black patches in an image like the one I attached here. Typical distance would be the the most frequent separation between two ...
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1answer
81 views

Image Registration / Fusion Optimal Similarity Metrics

I have a theoretical question about optimal similarity metrics for comparing data sets. In reading the linked pdf, I read the following 2 interesting statements: "In the ... scenario in which A and ...
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29 views

improve delay detection between two signals

Hi there I'm trying to measure time delay of one percussive event recorded by two contact mikes on a glass surface. I decided to check the cross correlation (via FFT) and detect the index of the max ...
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116 views

Problems filtering image with prewitt

I'm trying to filter an image vertically to get the edges, in MATLAB, but I get very different results from convultion and correlation. CODE: ...
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5answers
221 views

Find Short Clip of Audio Within Longer Clip Of Audio

I need help figuring out a way to automatically synchronize two audio files that are both different recordings of the same source. More info below. This example is from a concert, where there is ...
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1answer
81 views

Correlation between Sin and Square wave

I would like to know how $\frac T2$ came for time period in the image below.Because I think the frequncy is 1 so time period should be 1.Is that correct? or can anyone help me.. The article from ...
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4answers
157 views

Similarity between two Signals: cycle by cycle

I need to find the similarity between two signals, i.e., measured signal and the reference signal(e.g. a simple sinusoidal signal). What I mean by similarity is, if there is any decentralized glitch ...
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1answer
81 views

Image correlation confidence measure

I am trying to calculate the disparity between stereo image pairs. I'm using what appears to be the standard approach of correlating between a window of pixels from one image and a sliding window ...
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274 views

Why does a phase shift in the frequency domain not produce a time delay in the time domain?

Suppose I have an input signal which represents a vehicle front suspension response that has been measured using an accelerometer. It is seen that the measured rear suspension response is effectively ...
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1answer
121 views

Measuring the similarity of two waveforms [closed]

I have two approximately sine truncated waveforms of different amplitudes and I want a numerical measure of how similar they are to each other. I am sending a sonic pulse train whose multiple ...
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1answer
274 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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296 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
35 views

Timing synchronization in limited channel

I need measure timing of an signal that is send through a noise band limited channel (wireless). By measure timing, I mean measure as exactly as possible when the signal has arrived at the receiver. ...
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3answers
421 views

What does it mean exactly when two parts of a signal are correlated?

I stumble quite often upon the notion that two or more parts of a signal are correlated to describe semi-formally that they belong together. For example in image processing, two pixels on an edge ...
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1answer
84 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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320 views

What is obtained from the cross correlation plot?

Let’s assume that we have two audio signals, x(t) and y(t) affected by the noise as shown below. And we would like to cross-correlate these two signals and the cross-correlation plot is shown as ...
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1answer
184 views

calculate relative error of two signals [duplicate]

I'm new to dsp.stackexchange and digital signal processing. I'm required to develop an app to measure the similarity of two signals.for an example I need to compare breathing of a man whether it is ...
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76 views

Minimum Samples Per Chip?

Is there a 'Nyquist Criteria' for the minimum samples per chip that are needed for a correlator? I've heard 2, but will 1 work? What are the implications of having less than the minimum (in the ...
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What type of correlation is this equation?

In a book [1], gives an equation (equation 5.31 in the book) for estimating frequency offset in OFDM systems proposed by Classen. the procedure is: first, two OFDM symbols, $y_l [n]$ and $y_{l+D} ...
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3k 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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59 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 ...
3
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1answer
80 views

Extracting common signal from 4 sets of observations

I am working on a signal processing assignment where I need to find out one common time domain signal from 4 observation. The math is like this: \begin{array}{lcl} y_1(t) & = & a_1(t)*x(t) + ...
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1answer
34 views

Finding correct values based on information from two arrays

Consider the following scenario: Say, one machine is sending out a beep signal every 10 seconds in a very noisy environment. I have two sensors which detects these beeps independently. Device A is ...
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1answer
275 views

Using a Wiener Filter to Estimate a Transfer Function

As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, How would you put a minimum MSE criteria on how well the estimated filter weights ...
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Decompose stereo signal

Basically the same as this question, but it was never really answered: Stereo sound separation into three sources Imagine I have a really trivial signal: Left: 100Hz tone + 200Hz tone + 500Hz tone ...
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91 views

Wave Correlation?

I have an image processing application that is different than anything that I've done before, and am looking for suggestions on how to approach. Here is a basic description of the problem: Given a ...