Questions tagged [correlation]

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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second order cross correlation

I have two signal sequences $u$ and $y$, where the former is the input to a system and the latter is the output of the same system. I would like to find second-order correlation between the two ...
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Can white noise be correlated to a random signal

For an random signal $X$ (does not matter if it is correlated or uncorrelated), given lag $τ$. If white noise is added to this signal, then can the summation of them be a correlated signal? Also, even ...
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Cross-quantilogram method

What is this method in general? What is the main difference between the quantile cross-spectrum (QS) approach developed by Baruník and Kley (2019) and the cross-correlation function (QS) developed by ...
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Proving that the autocorrelation of a signal is the convolution with its time-reversed complex conjugate

I need to prove the property $$f(x)⊕f(x)=f(x)⊗f^*(-x)$$ That is the autocorrelation of a function is the convolution with its time-reversed complex conjugate. I have constructed most of the proof but ...
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How would the correlation coefficient between 2 images change if we rotated 1 image?

Suppose we have a image which is represented by a matrix $ \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix} $ and we want to find its correlation with ...
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Correlation gives contradictory results

I am trying to find the correlation between the signals $u(t)$ and $\sin(t)[u(t)-u(t-2)]$ The correlation function $C(t) = \int^{\infty}_{-\infty} u(\tau+t)\sin(t)(u(t)-u(t-2))d\tau$ This is my ...
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Average time-domain signal power from correlated Fourier transforms

Suppose I have real-valued continuous-time sequences $x_1(t), x_2(t), x_3(t)$ with Fourier transforms $X_1(\omega), X_2(\omega), X_3(\omega)$. I know that $X_3(\omega)=H(\omega)( aX_1(\omega)+bX_2(\...
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Template Matching non-rectangular template in non-linear order

Question Is there an existing algorithm that does cross correlation with two images, including a weight image? In template matching, when should I prefer the sum of absolute errors vs cross ...
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Correlating signals in real-time when the time-delay is larger than frame-time

What are some possible approaches to address the challenge of correlating two signals when the time delay ($T_d$) from the source to the microphone is greater than the microphone's frame time ($T_f$)? ...
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Model validation- comparing signals

Let's say I am trying to validate a model. I have a signal from measurement and a signal from the simulation of the model. Simulation was done with the same initial and boundary conditions as ...
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Could the conjugate derivatives of two independent random signals be uncorrelated?

Suppose there are two independent signals, $s(t-\tau)$ and $n(t)$, and they are doubtly uncorrelated so that $\mathbb{E}${$s(t-\tau)\times n(t)$}=0. I wonder if the equation $\mathbb{E}${$\frac{\...
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Calculating transform for maximum decorrelation?

Suppose you have a set of $n$ sensors with overlapping sensitivities--like the cone cells of an animal retina, which is in fact the sort of system I am trying to model. Given the frequency-response ...
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Ambiguity function volume

I find myself confused how two properties of the ambiguity function relate to one another. The properties in question are (presented here from wikipedia, but similar formulas can be found in books by ...
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Emergence - what constitutes a minimally coherent source that "just begins" to produce stationary interference patterns?

A superposition of two signals with different frequencies will never produce visible (i.e. stationary) interference patterns. Such waveforms will produce spatiotemporal beat patterns, but they rapidly ...
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What does the covariance of a power spectral density between frequency points mean [duplicate]

I am struggling to understand the meaning of the covariance of PSD (Power Spectral Density) between two frequency points ($f_1$ and $f_2$). The covariance of a function $s(t)$ in time domain $t$ is a ...
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Calculating delay b/w signals using correlation

I am generating two signals of same frequency, i introduce a fixed delay in one of the signal and then try to find out the simulated delay using MATLAB 'gccphat' and 'finddelay' functions, but not ...
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How can I check similarity of two different sinusoidal waveform model?

I am trying to establish a similarity index for two different signals. These signals are quite different in amplitude and signal length. Their waveform is sinusoidal, and frequencies are at a close ...
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Finding correlation coefficient of two dependent random variables

I know when there are two independent random variables X and Y, the correlation coefficient is But what if the two random variables are dependent, for example, Y-X and X+Y, how can I represent them ...
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Why we need convolution in image processing?

To my understanding, there are two methods to do linear filtering. One is cross-correlation, and another is convolution. Convolution requires 'flipping' the kernel when you do the calculation. I think ...
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What exactly happens in correlation?

I have understood convolution and it seems almost same as correlation mathematical expression wise. But in terms of signal processing,both are different operations. The difference between convolution ...
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The difference between convolution and cross-correlation from image processing point of view

The difference between convolution and cross-correlation from a signal-analysis point of view The above question gives very good information from signal processing point of view. But what about images?...
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Extract a signal from noise, so I can view noise spectrum only?

I have a perfect modulated signal. I have the same signal but with noise, this noise is from non linear amplification. Is it possible, to extract the clean signal so it's just leaving the noise? The ...
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Autocorrelation & Cross-Correlation -> Main uses in DSP??

Please help understanding the DSP usage of Autocorrelation & Cross-correlation It seems this is strongly linked to calculating phase offsets, frequency offset for carrier recovery, symbol timing ...
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Power spectral density and auto correlation function: Frequency vs time representation

I have a time correlated periodic signal $a(t)$ with $t=0,1,...,T$ and $a(t+T) = a(t)$ that has been sampled at rate $\Delta t$ and I analyse the signal using the PSD via FFT and the ACF. As far as I ...
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Cross-correlation maximum in frequency domain

I need to compute the complex cross-correlation between two signals a and b and the take only the maximum value of the cross-correlation, regardless of the lag time where this occurs. I can do it ...
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if I have 2 signals that are similar how will their cross correlation will look like?

I need to compare between 2 signals that both of them are different notes of the same musical instrument, so I thought maybe I can do it by Cross-Correlation but I dont really understand how to do it ...
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Generalized correlation coefficients

Assume there are given two Gaussian random vectors $\boldsymbol{x}$ and $\boldsymbol{y}$ of equal length $N$ with corresponding means $\boldsymbol{\mu}_x$, $\boldsymbol{\mu}_y$ and covariance matrices ...
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Plotting the real or absolute of correlation?

I had two vectors of data and I computed their correlation using corr(f,g) = ifft( fft(f) .* conj(fft(g)) ) / cov(f,g). I cannot figure out whether to use the real ...
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Y axis Component of Rxy in MATLAB

I calculated the $R_{xy}$ by cross-correlating $x(n)$ and $y(n)$. Now, in the MATLAB command window, I wish to construct the Y-axis component of $R_{xy}(n)$. I'm not sure how I'm going to do it. Is ...
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How can I generate X Axis componant in R_xy in MATLAB?

Let's say I have cross-correlated $x(n)$ and $y(n)$ and got the $R_{xy}(n)$. Now if I want to generate the x-axis component of $R_{xy}(n)$ in the command window of MATLAB. How can I do that? is there ...
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Is it possible to use a genetic algorithm for finding the correlation among time series

I am working on an optimized method for measuring the similarity between 2 signals, Is it possible to use a genetic algorithm for finding the correlation among time series?
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How to interpret values of the autocorrelation sequence?

I know that (auto)correlation indicates the "degree of predictability" of a variable with respect of another. However, this is a vague notion. I know that a blank process should have an ...
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How to find segment with specific speed on the signal in comparison with reference signal?

How do I find a segment on the signal where the signal speed is 2 times the speed of the same segment on a reference signal? Which features describe this? On attached image can see "change of ...
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Difference between reference and measurement signal?

Which differences can we find on various signals? We assume that we have a reference signal (determined theoretically) and measured signal. Which methods exist for determining the similarities ...
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Auto/cross correlation for data set with multiple realizations

Context For an assignment, I need to find the correlation matrix of a dataset with 100 random variables and 1000 realizations for each. (It's a stock market example). Problem I don't understand how ...
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MATLAB: How to compute the similarity of two signals and get the correct consistency or coherence metric

I was wondering about the consistency metric. Generally, it allows us to deduce the parity or similarity between two signals, right? If so, if the probability is higher (from 0.5 to 1), does it means ...
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Estimating Correlation Matrices

I am trying to obtain the correlation matrices of two random signals. Both of them, $ X $ and $ Y $, are white Gaussian Noise, with unitary variance. However, they are correlated, with correlation ...
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Correlation and the Fourier transform

In the book Fundamentals of Music Processing: Audio, Analysis, Algorithms, Applications by Meinard Müller, the coefficients $d_\omega$ and $\phi_\omega$ are defined as where $\cos_{\omega,\phi}(t) = \...
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Estimate the time delay of two signals

I am having 2 sets of data data1 and data2 .I wanted to find the delay between the two datasets. Assume data1=[1 2 3 4 5 6 7 8 9 10] and data2=[0 0 0 0 1 2 3 4 5 6].From the data I know that, data2 is ...
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Identify which of the three signals is closest to a sinusoidal curve

I have some acceleration values from a sensor. These values are reported as x, y and z components of the acceleration. As can be seen in the attached figure, it is clear that the z signal has a clear ...
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Correlation: A Magnitude or Power quantity?

I am confused about the units we would refer to with a correlation result in that if it would be a magnitude or power quantity (and therefore specifically when using ratios in dB would we use 10Log or ...
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When is the Correlation Coefficient Ergodic

Given Wide Sense Stationary (WSS) processes X and Y that are ergodic to the mean and autocovariance. Under what conditions is the correlation coefficient ergodic to the mean? ie: $lim_{T->\infty} \...
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Calculating cross-correlation using Walsh-Hadamard transform

I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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correlation matrix for complex white noise does not equal to identity matrix?

I generate 8 time series of gaussian white noise and want to compute the correlation matrix at a frequency bin between them. The following is the matlab code I use ...
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autocorrelation of multiple signals

Problem: I am looking at an adaptive filtering application where the eigenvaluespread of the autocorrelation matrix $R$ is important for the convergence of the algorithm. For a single channel system ...
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Why there is static noise and voice distortion after convolving it with impulse response?

I have been working on the decorrelation of audio signals while following this paper : The Decorrelation of Audio Signals and Its Impact on Spatial Imagery So far I have generated impulse responses in ...
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Do we assume modulating and carrier signal uncorrelated in AM modulation?

I am new to communication and studying amplitude modulation. Let us assume an amplitude modulated wave given by $$\big(m(t)+ A\big) \cos(2\pi f_c t)$$ Now we have formula for efficiency as $$ \eta=\...
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NaN values with correlation metrics

I am using the Peak to Correlation Energy (PCE) Metric to measure the similarity between two images using MATLAB. In some cases, the PCE value obtained is NaN. How can I solve this problem?
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How to measure correlation between 1 bit samples and theoretical original waveform?

I'm investigating quantization error. I have an analogue waveform that looks like this and is of theoretically infinite resolution:- I've sampled it as (8 bit oscilloscope readings & 0b1) to ...
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Linear correlation of two vectors?

We had a lecture on digital watermark detection using linear correlation. Here it was explained that the linear correlation of two vectors is equal to their scalar product divided by the dimension. So,...
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