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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Does this make sense for cross-correlation in frequency domain?

If I have a signal A at 2 kHz and signal B mixed at 2 kHz + 3kHz, and then i take the FFT of them both, and then cross-correlate them many times, the 3kHz peak should disappear? Since this peak is not ...
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How to verify if my cross-correlation algorithm works?

So I have a signal generator which can produce two separate signals. I use a spectrum analyzer to read these signals, and can interface with Python. I wrote a Python code which takes in these two ...
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How to extract information about each constituent 'wave' of a signal?

I have a vector containing wind speeds sampled at 1Hz over ten minutes. I have applied a lowpass filter of 0.25Hz to get only the wind speeds I am interested in. I now want to use MATLAB to ...
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194 views

Correlation Performed by Convolution

Background: The question here is related to images in particular and not signal/waveforms. I have been reading a lot of answers about the difference between convolution and correlation but I am stuck ...
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How can I get better results from Phase Correlation

I am using Phase Correlation to register 3D data. There's a clear distinction in the y direction so the resulting shifts seem to be correct. But since there is a lot of similarity in the x direction ...
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435 views

Finding dependence between two sparse signals

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 $X_1, \ldots, X_N$ and using this ...
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46 views

BER performance of fractional equalizers for colored noise

I am trying to compare the BER performance of fractional and symbol spaced equalizers for channel equalization in colored noise scenario. I have found from simulation that for positively correlated ...
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147 views

convolve to differentiate black and white colors

a figure for instance of size 500*500 has half above part with black and below half white should result in a white line where the white meets the black (something like a single line at line 250 with ...
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4answers
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Understanding correlation in image processing using examples

I have been trying to understand the intuition behind the correlation. I understand from this guide that correlation is a way to detect a known waveform in a noisy background. I have seen from this SO ...
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Can somebody explain SDF and MACE to me?

I can't find any information on SDF and MACE save for a vague exert in Kinser's Image Operators books. Therefore I am dumbfounded. I can't understand what they do and what's their role in composite ...
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125 views

What is the time reversal convolution

Given a signal $r(t)$ which is a result of convolution between signal $x(t)$ and a channel $h(t)$ as below : $r(t) = h(t)*x(t); $ what I know, the time reversal convolution can be process as ...
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192 views

How to get the background noise of microphone?

I am working on the automatic volume control for television which should take care of background noise. For this, I need to first find out the background noise. I have read in research papers that we ...
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Pearson correlation coefficient vs mutual information

I recently computed both the pearson coefficient and the mutual information of two time series as well as the corresponding error bars, and what I find out in the end is a significant level of ...
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Are there methods to measure how the change in one signal will affect another signal?

I have two distinct signals and I would like to compute their correlation. However, I think that just computing the crosscorrelation does not work here, since the signals are from different sources — ...
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Decorrelation for Adaptive Feedback Cancellation: How does it work?

I am going through lecture slides on adaptive feedback cancellation right now, and several decorrelation measures are mentioned. As I understand, these are important in order to avoid a bias in filter ...
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Find repeating sequences in audio file

I have a long audio file (12+ hours). I know that there are some unknown small (2 minutes each or thereabout, it varies) repeating (not bit by bit: it is recorded with a mic) chunks in it, repeating ...
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Practical question about DFT in Matlab

Please consider this piece of code: ...
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Validating Jakes model in Rayleigh Fading channels

I am trying to validate the Jakes model by comparing the autocorrelation function given by $ \rho(\Delta t ) = J_{0}(2 \pi f_{d} \Delta t)$, where $ f_{d} $ is the maximum Doppler shift, $ J_{0} $ is ...
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121 views

Correlation of independent random processes

Suppose $X(t)$ and $Y(t)$ be two independent random processes. Is $E(X(t_1)Y(t_2))$ necessarily zero?
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What is definition of independent random variable

I wan't to ask that if E{X}=0 E{Y}=0 and E{XY}=0 then how can I verify if the two random variables are independent or not. X , Y are both continuous random variables {I am not able to recall ...
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219 views

Maximum cross-correlation coefficient value for time delay estimation

I am using cross-correlation for time delay estimation of two synchronized recordings ($x_1$ and $x_2$) of a fixed sound source from two different locations. I understand that the delay is associated ...
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34 views

high & low pass correlated dither noise question

I read a pretty cool article the other day: https://www.digido.com/ufaqs/dither-noise-probability-density-explained/ It says that if you have two dice (A and B) that you can roll both dice and then......
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Combine correlating input signals to generate multiple output signals

Choosing a descriptive title was quite hard, as I am not sure how to describe my problem accurately. I have a mechanical system fitted with several sensors (Strain Gauges and motion Sensors). There ...
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How can i calculate a matrix of correlation?

I want to implement my own music algorithm detecting an angle of arrival of non-stationary signal and I need to make a matrix of correlation of this signal. I have problem because I don't know how to ...
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69 views

Signals Cross Correlation from Their Power Spectral Densities?

For two real valued signals $f$ and $g$ with their corresponding power spectral densities $|F(k)|^2$ and $|G(k)|^2$ Is there a way to get an intuition of how correlated $f$ and $g$ are just by looking ...
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Compressive Sensing - Incoherence Property

Compressive Sensing is built on 2 properties: 1) the sparsity of the representation basis relative to the sampling basis and 2) the incoherence between the singular vectors from each of the 2 bases in ...
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159 views

Cross Correlation, how can any signals except the trivial cases be uncorrelated?

I have been working on a problem where I am trying to subtract two Power Spectral Densities (PSD's) from one another in the following way. $$|F(k) - G(k)|^2 = |F(k)|^2 - |G(k)|^2$$ Which is only ...
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What kind of power spectrum implies uncorrelation in time?

I am new in signal processing field, and actually I just need some basic tools for what I am working on. I've learnt that the autocorrelation function is the inverse Fourier transform of the signal's ...
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Aperiodic Correlation function using FFT Method

Periodic correlation function between two binary sequences say x and y can be computed using FFT. corr_value = ifft(fft(x).*conj(fft(y)); Can some one please help on how to compute aperiodic ...
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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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Why is correlation involved? - Axis Rescaling for a 2D axes - brightfield illumination microscopy of blood cells

for 1D axis rescaling, you use a FOV calculation len_pixel=total_magnification * len_specimen_in_pixel len_specimen_in_pixel=len_pixel/total_magnification and then to get the axes rescaled, you do ...
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Time delay estimation of signals increasingly decorrelated

The problem may be summarized as follows: I have a stochastic signals and I want to measure an increasing delay, as depicted in the following picture. The picture represents the signal as it is being ...
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148 views

What is the Fastest Way Ever to Do 2D Correlation?

Here is what i gathered so far: Any sliding window classification, image filtering or similar can be fastly done by a FFT (flip the signal and do convolution). Also, if the template/filter kernel is ...
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What is the betwwen [i,j] and [u,v] in explinations of correlation and convolution (picture attached)?

I don't know how to write 'summation' symbol here hence posting the picture. Can someone explain to me the difference between i,j and u,v in this explanation of correlation and convolution? I know ...
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428 views

Matrix cross correlation in python

I'm currently performing matrix cross correlation in python using : C = scipy.signal.correlate2d(A,A) where A is a 2D matrix, typically a picture. As you can ...
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Efficient correlation of a low duty cycle training sequence

Is there a way to efficiently correlate a training sequence that is N samples long, framed at M samples where M >> N, with L occurrences of such frames (see below). For the pedants, the training ...
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103 views

What is the difference between using corrcoef to compare two signals by column, and as whole matrices?

I have two matrices, which represent acceleration readings of the same event from two seperate sensors, and I would like to calculate the correlation coefficients so that I may get a measure of how ...
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Why do we need to conjugate complex signals in autocorrelation and cross correlation

Why is it necessary to conjugate $f(t)$ while performing auto correlation or cross correlation with respect to $g(t)$, if $f(t)$ and $g(t)$ are complex signals?
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72 views

Detection complex vectors by using correlation

I sent out a complex vector $x_i \in \{x_1,...x_n \}$ and receive a vector $y$. I use correlation $y^Hx_i$ to detect which $i$ was sent. If $y$ is corrupted by AWGN channel, the optimum rule should ...
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989 views

Phase Correlation and Negative Shifts

I am implementing phase correlation algorithm to determine shift between two images. It generally works, but I am not sure how to interpret the resulting shift. Pseudocode: ...
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Co-prediction of signals

Is there any plausible method to estimate or predict one signal, on the basis of known value of another signal, provided the two signals bear a strong correlation? For instance, the audio amplitude ...
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98 views

Correlation between slightly misaligned images

I am matching camera images of projection screens with rendered pages of PDF documents using Pearson's and Spearman's correlation coefficient. When the images (3, 4, 5) are aligned, this works fine in ...
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Physical interpretation of 4th-order correlations

BACKGROUND: Let's say we have samples of a random process $X(t)$ at two different times, $t_1$ and $t_2$, denoted $X(t_1), X(t_2)$. The values of $X(t)$ represent some voltage-like quantity (i.e. a ...
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93 views

Two different definitions of cross-correlation

I have come across two different definitions of the cross-correlation function: $$ R_{XY}(\tau) = \int_{-\infty}^{+\infty} x(t) y(t+ \tau) dt $$ and $$ R_{XY}(\tau) = \int_{-\infty}^{+\infty} x(t)...
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How can faux correlated data be generated for testing or training?

There are one or two questions here that ask how to assess data correlation. The data tends to be empirical. Is there some tool or standardised technique for generating correlated data from scratch? ...
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195 views

How do I know quantitatively if the correlation of two time series is significant?

I computed the correlation coefficient of two time series of daily observations, x and y, but noticed that the more sampling ...
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81 views

What level of correlation coefficient suggests correlation?

In Python (and Numpy), I recently did:- a = np.random.randint(0,256,1000) b = np.random.randint(0,256,1000) and when I calculate the correlation coefficient $r$ ...
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61 views

How to interpret correlation angle from frequency domain

Since the coefficient of one frequency could be seen the length of the signal projects on that frequency basis. And the length is $$|a|\cos\theta= \frac{a\cdot b}{|b|} $$ If I divide the ...
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139 views

Correlation of a signal

I have one sample for a signal. This sample is a vector of length 384. I need to calculate the correlation matrix for this signal,So I need many samples for the same signal. How can i generate these ...
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231 views

Is there anything called uncorrelated filter?

I understand to an extent various filter like low pass filter, high pass filer, Wiener filter Kalman filter etc. I also understand some of this filter will decorrelate/uncorrelate the signal. The ...