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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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1 answer
257 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 ...
0 votes
2 answers
399 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 ...
0 votes
0 answers
22 views

How to sync two similar lists/waveforms with differently populated data in python?

I have two lists of sizes L1 - 22400(865*26) and L2 - 79000 with measurements of some environmental data. Data of both the lists are measured simultaneously. The L2 is a continuous measurement for ...
0 votes
1 answer
52 views

Wrong matched filter sidelobe level for linear chirp despite (invalid ?) energy normalization

I'm trying to reproduce the -13.2 dB sidelobe level typically observed for a linear chirp pulse (cf. for instance this MATLAB documentation page: ...
0 votes
0 answers
29 views

How can I calculate the probability of detection and false alarm rate of a correlation result assuming a given SNR threshold in AWGN?

I am transmitting an LFM chirp with fixed bandwidth $B$ and sample rate $f_{s}$, containing $N$ samples. The chirp is windowed with a Kaiser window, which generally has constant $\beta$ but can vary. ...
0 votes
1 answer
121 views

Cross Correlation Peak Value of Wideband signals - The Phase and Sample Offset are related but how

Two CDMA Codes or Gold Codes or PRN Sequencies, i.e. a pattern in time, are cross correlated in the time domain. However one of them is delayed compared to the other. How is the phase argument of the ...
0 votes
1 answer
56 views

Cross-correlation of two processes generated from the same signal through different LTI systems

A problem in Statistical and Adaptive Signal Processing (problem 10.15) presents two WSS signals both generated from zero-mean white Gaussian noise with $\sigma_w = 1$. They are described by $v_1(n) = ...
1 vote
2 answers
10k views

How to normalize output of $\tt scipy.signal.correlate$

I have 2 different signals and I'm trying to cross-correlate then using Python 2.7 and scipy.signal.correlate. How do I normalize my results (such that the max ...
2 votes
1 answer
107 views

Correlation gives contradictory results

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 ...
1 vote
0 answers
95 views

second order cross correlation

I have two signal sequences $u$ and $y$, where the former is the input to a system and the latter is the output of the same system. I would like to find second-order correlation between the two ...
2 votes
1 answer
1k views

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 ...
-1 votes
1 answer
162 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 ...
1 vote
1 answer
295 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 ...
0 votes
0 answers
42 views

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 ...
0 votes
1 answer
80 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 ...
2 votes
0 answers
42 views

Average time-domain signal power from correlated Fourier transforms

Suppose I have real-valued continuous-time sequences $x_1(t), x_2(t), x_3(t)$ with Fourier transforms $X_1(\omega), X_2(\omega), X_3(\omega)$. I know that $X_3(\omega)=H(\omega)( aX_1(\omega)+bX_2(\...
0 votes
0 answers
41 views

Template Matching non-rectangular template in non-linear order

Question Is there an existing algorithm that does cross correlation with two images, including a weight image? In template matching, when should I prefer the sum of absolute errors vs cross ...
2 votes
0 answers
217 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 ...
2 votes
1 answer
380 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?...
0 votes
2 answers
70 views

Correlating signals in real-time when the time-delay is larger than frame-time

What are some possible approaches to address the challenge of correlating two signals when the time delay ($T_d$) from the source to the microphone is greater than the microphone's frame time ($T_f$)? ...
2 votes
3 answers
2k views

Synchronization of two audio tracks via Mel-frequency cepstral coefficients (MFCCs)

I am trying to solve the (common) problem of synchronizing (i.e. measuring the delay between) two audio tracks recorded from different sources during a conference talk (about 1h of audio). One track ...
0 votes
0 answers
27 views

Model validation- comparing signals

Let's say I am trying to validate a model. I have a signal from measurement and a signal from the simulation of the model. Simulation was done with the same initial and boundary conditions as ...
1 vote
0 answers
38 views

Could the conjugate derivatives of two independent random signals be uncorrelated?

Suppose there are two independent signals, $s(t-\tau)$ and $n(t)$, and they are doubtly uncorrelated so that $\mathbb{E}${$s(t-\tau)\times n(t)$}=0. I wonder if the equation $\mathbb{E}${$\frac{\...
3 votes
1 answer
58 views

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 ...
3 votes
0 answers
134 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 ...
2 votes
1 answer
546 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 ...
5 votes
3 answers
14k views

Cross correlate a 2D array

I have a 2D array of eeg data with shape (64,512) - 64 electrodes, 512 timepoints I want to calculate the maximum cross correlation (irrespective of lag/time shift) between every single electrode, so ...
0 votes
1 answer
45 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 ...
2 votes
1 answer
2k views

Why correlation is not associative in the context of image processing?

I can see most of the places it says "convolution is associative, while correlation, in general, is not". Denote $*$ convolution operator, let's say you have an image $f$, which you need to convolve ...
1 vote
1 answer
391 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 ...
0 votes
0 answers
46 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 ...
0 votes
2 answers
196 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
1 answer
150 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 ...
4 votes
1 answer
11k views

numpy.correlate and autocorrelation; audio signal

I want to calculate delay between an input and an output audio signal of my audio processing system. The input and output signals are available as signed 16 bit integers. To try out, I tried the ...
0 votes
2 answers
139 views

Extract amplitudes

I have two mixed signals like $A_1f(t) + A_2g(t)$, where $f(t)$ and $g(t)$ are sinusoidal. I want to extract the amplitude infos. Directly I can not get the amplitudes (or I don't know how to). What I ...
3 votes
2 answers
345 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 ...
1 vote
1 answer
130 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 ...
0 votes
2 answers
562 views

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 ...
2 votes
2 answers
610 views

Comparing two small audio files (e.g., hand clap) Android

Dears, I am new in signal processing and I am dealing with an Android application that should do some audio files (having the same "small" duration) comparison in real time. My main focus is ...
5 votes
1 answer
881 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 ...
5 votes
1 answer
725 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 ...
-1 votes
1 answer
582 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 ...
2 votes
1 answer
78 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 ...
0 votes
2 answers
459 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 ...
0 votes
1 answer
58 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 ...
-1 votes
1 answer
54 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 ...
-1 votes
1 answer
145 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
1 answer
448 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 ...
2 votes
1 answer
263 views

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 ...
3 votes
2 answers
108 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 ...

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