10 votes

What is the difference between convolution and cross-correlation?

As a student I was involved in the same problem as you are. Let me explain to you in the simplest words without any math. Convolution: It is used to convolute two function. May sound redundant but I´...
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Auto Correlation vs Cross Correlation vs Convolution and their applications

I can tell you of at least three applications related to audio. Auto-correlation can be used over a changing block (a collection of) many audio samples to find the pitch. Very useful for musical and ...
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perfect sequences

Let $\theta_a$ and $\theta_c$ respectively denote the maximum magnitudes of the off-peak or out-of-phase periodic autocorrelation functions and the periodic crosscorrelation functions of a set of $K$ ...
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Autocorrelation of Addition of Two Independent Signals

You're correct as the Cross Correlation function vanishes. This has the implicit assumption the process has zero mean (Actually, at least one of them). Namely, in order to have $ {R}_{XY} \left( \tau ...
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Correlation of independent random processes

No. Quoting Wikipedia's article Independence (probability theory): If $X$ and $Y$ are independent random variables, then the expectation operator $\operatorname{E}$ has the property $$\...
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Detecting a Signal Inside a Time Series Using MATLAB's $ \tt xcorr() $

The function xcorr calculates the correlation of 2 signals. The correlation is known to be a good (The MLE) for delay estimation under Gaussian Noise. Yet, as ...
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Python - Normalized cross-correlation to measure similarites in 2 images

I guess you can compute for each pixel the correlation coefficient between patches centered on this pixel in the two images of interest. Here is an example where I downloaded the figure attached here ...
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How to calculate a delay (correlation peak) between two signals with a precision smaller than the sampling period?

This is basically what @hooman suggests: fit a parabola to the three points near the peak of the sample cross-correlation of the data. Using the formula for $p$ here: $$ p = \frac{1}{2} \frac{\alpha -...
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Cross correlation, when two signals are "uncorrelated"?

Cross correlation is a measure of similarity between two signals, where one signal is allowed to be time-shifted. In this sense, the correlation is not a single number, but a function of the time ...
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6 votes

FMCW Radar Signal Processing Flowchart / Ambiguity Function

The Ambiguity Function is just a name for 2D Correlator. It is known that given a shifted 1D Signal the optimal estimator for the shift (Range in RADAR / LIDAR, etc...) it the correlation with the ...
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Comparing multiple signals for similarity

...best results come from a weighted ensemble of techniques... Maybe they do, depending on the application. But each one of the similarities mentioned, is equivalent to the other at least when we are ...
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6 votes

Cross-correlation seems defined backwards

Interesting question. For purposes of "pattern matching" the resulting peak of the auto-correlation function will either be consistent with the actual time offset between the matching ...
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5 votes

Meaning of the Transpose of Convolution

If you have convolution given by: $$ \boldsymbol{y} = \boldsymbol{h} \ast \boldsymbol{x} $$ You can transform it into Matrix Form: $$ \boldsymbol{y} = H \boldsymbol{x} $$ Then the operator $ {H}^{...
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How is cross-correlation related with orthogonality?

I suppose you mean the cross-correlation at lag zero. Well take an Hilbert space $H$ (i.e. a metric space in which you can define a scalar product $\langle\cdot ,\cdot\rangle$). Then $x,y\in H$ are ...
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Cross-correlation or cross-covariance of non-zero mean signals

What are reasons to choose for cross-correlation or cross-covariance when comparing signals with non-zero mean? Well, part of the issue is that cross-correlation as defined in your equation: $$(f \...
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How can define an indicator which measures the degree of similarity between two signals?

The general topic of finding similarities between signals is wide ranging: are the signals of same sampling, length, offset, shift or scale? where do they take their values (discrete, real, complex)?...
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5 votes

How to calculate a delay (correlation peak) between two signals with a precision smaller than the sampling period?

Lagrange parabolic estimator The standard Lagrange polynomial parabolic interpolation peak finding formula from Peter's answer, $$p = \frac{1}{2} \frac{\alpha - \gamma}{\alpha - 2\beta + \gamma}$$ ...
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Cross correlate a 2D array

What you have (conceptually) is not a 2D array but a collection of 1D arrays. correlate2D is designed to perform a 2D correlation calculation, so that's not what ...
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5 votes

Pixel Wise Write into a Video File in MATLAB

I assume your matrix is 3D where the first 2 dimensions are Width and Height and the third is time (Gray Scale Video). If you can write your processing as a Filter you can use MATLAB's ...
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When to use cross spectral density versus cross correlation?

The cross-spectral density is in the frequency domain while the cross-correlation function is in the time domain. The two are Fourier Transform pairs, the FT of the cross correlation function is the ...
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What Does It Mean When Cross Correlation Between Two Images Occur at Negative Coordinates

It means the best match to template happens outside the image. For instance, let's say your template is 5 by 5. And you got answer which is -1, -1. It means the part of the image which best matches ...
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Matched filter and cross correlation in digital processing

I'll illustrate with an example: detecting a rectangular pulse in noise, in Matlab. Let's start with defining the signal that contains the pulse. ...
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Maximum cross-correlation coefficient value for time delay estimation

As your plot shows, the second form allows for the correlation peak to be negative. Now, what does a strong negative cross correlation mean? It means the signals are very similar, except one has a ...
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How to reliably compute the group delay of a comb filter

Since this is an FIR, the group delay is D=(N-1)/2=20 samples. No, since this is a linear phase (i.e. symmetric or anti-symmetric) filter, the group delay is half the length! (being a FIR isn't ...
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Is `xcov()`More Accurate Than `xcorr()` to Compute the Cross Correlation of Signals with Non Zero Mean Values?

When trying to measure similarity between signals we're basically building a metric. When doing so we need to ask what we want to be sensitive about. For instance, if you don't remove the DC Component ...
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"cascaded" cross-correlation

I'm afraid your statement isn't true. This can best be seen in a suitable choice of basis, one that simplifies the cross correlation. This basis if of course the shift invariant periodic Fourier basis ...
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4 votes

Least Squares and Auto and Cross Correlation

Indeed the Linear Least Squares uses the Covariance (Which resembles Cross Correlation) and the Variance (Which resembles the Auto Correlation) for parameter estimation. Let's see that using simple ...
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Baseline correlation for template matching

This would be a cumbersome way to detect heart beats (or the QRS complex), if that is what you are trying to do ultimately. A little bit about what you are trying to do currently: Your observations ...
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Computing cross-correlation of two images using OpenCV

On closer inspection, I discovered that the erroneous correlation result resembles the correct result, but shifted up and to the left. The former was displayed in scientific format, so it was hard to ...
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  • 481
4 votes

Detecting a Signal Inside a Time Series Using MATLAB's $ \tt xcorr() $

It is usually useful to use normalized cross-correlation for finding position of small template on other longer signal. The value of normalized cross-correlation coefficient is invariant to change of ...
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