# 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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### 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 ...
1 vote
132 views

### 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 ...
56 views

### 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 ...
1 vote
78 views

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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### 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 ...
204 views

### 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 ...
132 views

### 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 ...
252 views

### 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 ...
40 views

### 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 ...
1 vote
180 views

### 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 ...
44 views

### 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 ...
143 views

### 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 ...
1 vote
104 views

### 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 ...
150 views

### 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?...
250 views

### 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 ...
270 views

### 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 ...
312 views

### 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 ...
1 vote
390 views

### 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 ...
57 views

### 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 ...
105 views

### 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 ...
1 vote
104 views

### 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 ...
133 views

### 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 ...
65 views

### 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?
1 vote
438 views

### 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 ...
30 views

### 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 ...
1 vote
401 views

### 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 ...
48 views

### 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 ...
150 views

### 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 ...
46 views

### 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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### 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 ...
179 views

### 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 ...
192 views

### 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 ...
287 views

### 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 ...
1 vote
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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=\...
127 views

### 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 ...
1 vote