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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Autocorrelation function and correlation integral

I am confused by the definition of autocorrelation function. It is originally defined as the expected value $$R_{XX}(\tau) = E[(X(t)X(t+\tau)] = \langle X(t)X(t+\tau)\rangle\tag{1}$$ where $\langle\...
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argmax of the cross correlation

I want to find the shift between 2 signals $\sin a$ and $\sin b$ where (with Matlab code) $$ a = \{0, 1,2,3,4\} $$ $$ b = a +1 $$ $$ \implies b = \{1,2,3,4,5\} $$ then $$ \arg\max \sin a = 2 $$ and ...
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26 views

Correlation of discrete time periodic sequences

So I was reading this textbook - Digital Signal Processing by Proakis and Manolakis. The authors define the cross-correlation operation for 2 energy signals $x(n)$ and $y(n)$ in section 2.6.1 as: $$ ...
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Correlations of matrix

I have a matrix of 10 column, each column has measurements at different times. I have a second matrix also of 10 columns, each consisting of measurements at different times. I want to carry out cross ...
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43 views

How to find if the signals are in sync or out of sync with each other?

Considering these are two signals over time, black and red.Following are some of the properties Every Second a new data point is added over time . There is no control on the generation of the ...
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37 views

Determine reflections from received signal

I have a reference signal $r(t)$ and the correlation between that reference signal and the received signal : $C_{XR}(\tau)$. The signal I receive contains reflections on walls. I have to build a ...
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66 views

Kronecker delta instead of dirac delta as correlation function of white noise

From my understanding, if you have a sample $x_{t_1},\dots,x_{t_n}$ of $X_{t_1},\dots,X_{t_n}$ which are iid $N(0,1)$, then $x_{t_1},\dots,x_{t_n}$ is a sample path of Gaussian white noise. However, ...
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Autocorrelation - Understanding reduced correlation at periodic time shifts using np.correlate (versus statistical autocorrelation)?

I'm going through the Think DSP by Allen B. Downey, and I'm struggling to understand a specific aspect of np.correlate and how it differs from statistic autocorrelation. The question is at the bottom, ...
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66 views

Solving nonlinear Fourier relation

I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$: $S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$ with $n&...
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39 views

Dependence of correlation peak height on GPS C/A signal's SNR, noise floor level (dBFS), correlation period length and ADC resolution

Assuming correlation at 2X the chip rate (2046 chips per period) and 500 Hz frequency search bins. There are probably additional variables here that I'm missing and I'm not sure how to quantify a ...
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43 views

Detect orthogonal sequence with fading

For a set of $N$ orthogonal sequences $\textbf{A}^i = \{a_1^i,a_2^i,...,a_M^i\}, i =1 ..N$, the detection of these sequences can be done by calculating the inner product (dot product) of receive ...
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53 views

What is the explanation for the inverse FFT of a cross-correlated signal being shifted by some amount in the time domain?

I created two signals in the time domain: signal A which is a square wave, and signal B which is a right-angled triangle wave, as shown in the picture below. I took the FFT of these signals, ...
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169 views

convolution vs correlation? [duplicate]

What is difference between convolution and correlation?In simple words or in a nut shell? As far as i am able to study is that Convolution is a mathematical operation used to express the relation ...
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19 views

How can I calculate time gap in different waves

I want, calculate the time gap between two signals .but that signal has frequently changed the frequency range. I want to combine with these two signal including phase shift I have a circuit for ...
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70 views

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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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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4answers
146 views

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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228 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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25 views

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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39 views

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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137 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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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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102 views

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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271 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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41 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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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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82 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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165 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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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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192 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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77 views

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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171 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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205 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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1answer
81 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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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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89 views

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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100 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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86 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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64 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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177 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 ...