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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Self-correlation vs Digital frequency: figure from paper
In the paper, is discussed a MIMO-OFDM system over the frequency self-correlation of i.i.d. Rayleigh
channels and subcarrier grouping. in this paper is shown the following figure.
it shows the self-...
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Spatial multiplexing MIMO, antenna critical spacing, antenna isolation
How does antenna isolation affect single user spatial multiplexing MIMO performance in an antenna array? Text books talk about a critical antenna spacing of 1/2 of the wavelength provided that the ...
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Noise and harmonic elements w/in a discrete time signal
So I have a discrete-time signal with around 300 samples. It is part of an environmental science application, so is not-strictly periodic although there clearly are periodic components. I have applied ...
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nature of output of the addition of white noise with colord noise
I want to know that the addition of a uncorrelated time series x with a correlated time series, say y generates a time series ...
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Proving that FFT (and by extension any correlation based estimator) is unbiased
I have a pretty simple question which i should have been able to answer. Just wanted to check if people here have a better solution to it.
I am trying to establish that FFT as a frequency estimator (...
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Comparing mechanical signals with different length
I couldn't find any solution for this that would work for me
I'm working in python.
I have two similar signals that I can plot Force x Angle. (problem simplified)
One plot (angle x force) has length ...
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How does Correlation for 1D Signals work?
On page 2 of the slide, I don't understand the example. Like $j$ and $s$ are both on the x-axis, what does j+s mean? The filter is $(f(−1), f(0), f(1)) = (−0.5, 0, 0.5)$. How can we use it? Could ...
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correlation matrix vs. correlation function?
Can someone help me understand the difference between a 1-dim autocorrelation function and a 2-dim autocorrelation matrix of a random process aka time series?
My Leon-Garcia textbook defines CX(τ) and ...
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Are ACF plots sufficient to detect white noise assuming probable existence of non linear associations?
ACF plots use autocorrelations tests to determine associations in time series. Autocorrelations, however, only measure linear associations. To my understanding, certain non-linear associations can ...
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How does DCT decorrelate images?
I've read in multiple places that DCT decorrelates Toeplitz matrices and images usually have Toeplitz structure. Can you explain with an example how DCT decorrelates a Toeplitz matrix?
Example for DFT:...
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34 views
packet encoder RF packets by using LPF for determining if it's zero or one [closed]
I'm transmitting RF packets with frequency 868MHZ ,
symbol rate (it's the same as bit rate) is 50KBaud , and Im sampling them by a dongle (fs=20480KHZ) to capture those RF packets, the captured ...
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46 views
Deciding if the received packet is valid or not valid [closed]
I have sampled RF wireless packets as IQ samples file, those RF packets has patterns like preamable|syncword|data|crc , I'm doing cross correlation with my constant syncword (after I did the ...
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Find Syncword (pattern) in signal, using Correlation
I have a signal which always has the same syncword ([93 0b 51 de] in hexa).
I also have a signal with additive noise(attacing it, and I want to find my syncword in that a noisy signal using corelation(...
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1answer
22 views
Correlated fading channel: transmit and receive antenna correlation matrices
I am trying to create a non-i.i.d channel: correlated Rayleigh fading channel.
$$ H= R_H \cdot H_o,$$
where $H_o$ is i.i.d. channel ( uncorrelated) and $ R_H$ is a channel correlation matrix, is ...
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2answers
148 views
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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1answer
31 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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34 views
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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47 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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1answer
47 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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1answer
88 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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50 views
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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67 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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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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75 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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1answer
311 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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23 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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1answer
81 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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367 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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1answer
348 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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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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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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150 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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112 views
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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4answers
107 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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1answer
315 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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1answer
42 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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40 views
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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24 views
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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89 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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171 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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1answer
96 views
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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1answer
241 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 ...
