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.
179
questions
3
votes
1answer
33 views
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:...
0
votes
1answer
30 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 ...
0
votes
1answer
39 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 ...
1
vote
0answers
80 views
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(...
0
votes
1answer
19 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 ...
0
votes
2answers
76 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\...
0
votes
0answers
18 views
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 ...
1
vote
1answer
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:
$$ ...
0
votes
1answer
33 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 ...
1
vote
0answers
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 ...
0
votes
1answer
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 ...
0
votes
1answer
74 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, ...
0
votes
1answer
40 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, ...
2
votes
0answers
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&...
0
votes
1answer
41 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 ...
1
vote
0answers
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 ...
0
votes
1answer
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, ...
1
vote
1answer
178 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 ...
0
votes
0answers
21 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 ...
0
votes
1answer
71 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 ...
0
votes
1answer
50 views
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 ...
1
vote
0answers
51 views
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 ...
0
votes
0answers
21 views
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 ...
3
votes
4answers
201 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 ...
1
vote
1answer
245 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 ...
1
vote
0answers
27 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 ...
0
votes
0answers
35 views
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 — ...
0
votes
0answers
28 views
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 ...
0
votes
0answers
43 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 ...
0
votes
1answer
80 views
2
votes
1answer
142 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?
0
votes
1answer
100 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 ...
0
votes
4answers
105 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 ...
5
votes
1answer
277 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 ...
0
votes
1answer
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......
0
votes
0answers
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 ...
0
votes
1answer
21 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 ...
0
votes
1answer
84 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 ...
1
vote
1answer
166 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 ...
2
votes
1answer
92 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 ...
1
vote
0answers
60 views
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 ...
3
votes
1answer
196 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 ...
0
votes
2answers
90 views
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 ...
0
votes
1answer
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 ...
0
votes
0answers
188 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 ...
1
vote
1answer
220 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 ...
1
vote
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 ...
0
votes
0answers
47 views
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 ...
4
votes
1answer
90 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 ...
0
votes
2answers
101 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)...
