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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2answers
6k views

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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177 views

Difference between $\mathbb{E}[\mathbf{x} \mathbf{x}^{\rm{H}}]$ and $\mathbb{E}[(\mathbf{x}-\boldsymbol{\mu}) (\mathbf{x}-\boldsymbol{\mu})^{\rm{H}}]$

Let us have a random vector $\mathbf{x} \sim \mathcal{CN} (\boldsymbol{\mu}, \boldsymbol{\Sigma})$ with $\boldsymbol{\mu} \neq \mathbf{0}$. What can we say about the relationship between the elements ...
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1answer
267 views

Why MATLAB only allows cpsd and mscohere between vectors with the same length?

I am studying the applications of finding coherence in the frequency spectrum between two signals for pattern recognition. I have a recording that is way longer than the sampled signal that I want to ...
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1answer
1k 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 ...
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0answers
267 views

Fastest PC configuration for FFT [closed]

I'm currently implementing rotation-invariant phase correlation algorithm, which is a variant of phase correlation algorithm (https://en.wikipedia.org/wiki/Phase_correlation) to estimate relative ...
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1answer
2k views

what does it mean to have a decorrelated colour space?

I'm working on the problem of colour transfer between images. In the literature there's a common practice that consists in performing the transformations on images in what is called a decorrelated ...
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2answers
302 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 ...
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1answer
2k views

Obtaining impulse response by means of cross-correlation between input and output

Having a system with an input (sound emitter) that is defined as a unit-variance white noise sequence, and I get the output (sound receiver) so I can measure cross-correlation functions between them, ...
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1answer
144 views

perfect sequences

I have heard somewhere that sequences with perfect autocorrelations and crosscorrelations do not exist. I have been searching for an insight into this claim, but have not been successful. Can anyone ...
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1answer
1k views

Array Signal Processing: What are snapshots in Direction of Arrival estimation?

I do have an overview of basic radar signal processing chain [Data cube, 3 stages of FFT, Range, Range-Doppler map, coherent/non-coherent integration, coarse DoA etc.]. I am now trying to understand ...
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1answer
517 views

Question about correlation of two signals

I'm working on some practice examples and in one of them I'm asked to find the convolution and the correlation of some signal pairs given. I know that correlation , given two signals x(n),g(n), is ...
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1answer
191 views

Recovering a DSSS signal with poor clock synchronization

I've run a lot of simulations and it seems like DSSS is just as noise resistant as people say it is. Resistant from jamming and even it seems some fading and narrow-band interference. I'm doing this ...
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1answer
6k 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 ...
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1answer
4k views

Correlation of two signals at different sample rate

I have a signal $X$ and I want to find signal $Y$ in $X$, I can achieve this by cross-correlation. Signal $X$ is sampled at $8000\textrm{ Hz}$, and $Y$ signal is sampled at $44100\textrm{ Hz}$. My ...
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1answer
894 views

Correlation (or something similar) analysis between data with different sampling rates

I tried to do correlation analysis on the data with different sampling rates. For example, I have two sensors, A and B. Each sensor collects data with different sampling rates, e.g., A: 10Hz, B: 1Hz. ...
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1answer
2k views

Find Preamble (pattern) in signal, using Corelation

I have a signal which always has the same preamble (4x 0xAA - 10101010...). I also have a signal with additive noise, and I want to find my preamble in that a noisy signal using corelation. U used ...
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1answer
202 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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1answer
2k views

Angle of arrival (AOA) estimation using FMCW radar using MUSIC algorithm

I am working with FMCW phased array radar with only upchirps. The range doppler matrix is obtained using the two dimensional fast Fourier transform on multiple chirps. I want to obtain the angular ...
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1answer
882 views

Is there any difference between using convolution and correlation for finding edges with Sobel?

I know that Sobel is a filter for edge detection and we should use convolution to find edges, but is there any difference if we use correlation instead of convolution? I think Sobel tries to find a ...
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1answer
9k views

Correlation : How is correlation analogous to dot product?

Till now I know correlation tells about similarity. I was watching a video lecture on image similarity in which I came to know that correlation is analogous to dot product. And hence correlation of ...
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1answer
156 views

Matching guitar signal with tablature, near real-time algorithms?

I'm looking for candidate algorithms that might work for a use-case comparable to Rocksmith's analysis system. To compare a clean electric guitar signal with a tablature reference. A higher latency ...
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3answers
250 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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2answers
9k 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 ...
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3answers
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What is meant by "correlation" when referring to spectral coherence

I've been reading that coherence measures the correlation between two waves as a function of frequency. I also read that difference in phase does not mean less coherence at a given frequency, and that ...
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1answer
3k views

correlation coefficient between these two signals [closed]

hello there can anyone tell me how to find correlation coefficient between these two signal using equation?? i don't know how to find correlation coefficient between these two signals. i checked ...
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0answers
67 views

Correlation between a lowfrequent and a fast signal

I need to evaluate the correlation between some measured signals. Those signals are for example current, temperatures at various points, vehicle speed and torque from an electric motor in a vehicle. I ...
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1answer
106 views

Cross Correlation [closed]

I have two signals which I obtained from a State Estimator and the one the measured one "actual signal obtained from the nodes. I need to compare between the two signals how similar they are . or if ...
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1answer
1k views

Tied rank adjustment for Spearman Correlation

I have two 16 sample vectors, a and b as listed below: ...
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1answer
3k views

Cross-correlation or cross-covariance of non-zero mean signals

Cross-correlation for uniformly sampled signals is defined as [1] $$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$ Cross-covariance for wide-sense stationary (...
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1answer
431 views

Correlated Noise

I have a vector of samples $Y[n]$. Then a fraction of delayed version of this vector added to itself: $$Y_\text{noisy}[n] = Y[n]+ aY[n-m]$$ The term $Y[n-m]$ considered as a correlated noise. How ...
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2answers
808 views

Why correlation property of $\mathcal Z$-transform contains a time reversal operation

I'm reading through Digital Signal Processing, Proakis and Manolakis, third edition. I've reached section 3.2: Properties of $\mathcal Z$-transform. One property is the convolution: $$x(n) = x_1(n)\...
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2answers
3k views

Practical advices for applying phase correlation in image registration task

I'm using OpenCV to detect shift between 2 images, here is sample code (based on cv::phaseCorrelate function): ...
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1answer
111 views

How to find the time instant where my sent signal and received signal can synchronize?

I am having two .wav files, one is modulated wave that is made into a .wav file and another is a recieved .wav file which is recorded from microphone while playing first modulated .wav file. So now ...
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1answer
1k 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 ...
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3answers
240 views

Phase shifting a noisy signal

I have a signal of the form $s(t)=A(t) \sum \cos(\omega_i(t)t +\phi_0) + n(t)$, where $n$ is gaussian noise. I can only read the signal+noise and thus can not separate them. I want to phase shift ...
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2answers
2k views

Signal correlation vs Pearson correlation between signals

I have some data which are the sets of values uniformly distributed along some measure (simple example - along the time intervals). I tested both the coefficients and found the difference, some times ...
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0answers
54 views

Pearson correlation of neural responses with it's linear estimation

I am trying to understand the following fact from this article (page 13): How can single neurons predict behaviour Suppose I have a linear estimation of a stimulus: $ \hat{s} = \mathbf{w}^T(\mathbf{r}...
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1answer
300 views

How to implement Cross Spectral Density [duplicate]

I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image. Reading wiki1,wiki2,wiki3 from wikipedia, and ...
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2answers
976 views

Why is autocorrelation used without normalization in signal processing field?

According to the wikipedia(Link), autocorrelation has two definition. In statistics, the definition of the autocorrelation between times $s$ and $t$ is like the following: $$\displaystyle R(s,t) = \...
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0answers
63 views

Eigenvalues of correlation matrix which have the form of an harmonic function [duplicate]

As a continuation to this question, I took the matrix $C_{2 \times 2}$ which is: $$C=\left[ \begin{array}{} a& ace^{-\frac{|\phi_1-\phi_2|}{2}}\\ ace^{-\frac{|\phi_1-\phi_2|}{2}} &...
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1answer
374 views

How do I calculate the eigenvalues of a covariance matrix which contains harmonic functions

I have read that $ce^{-\frac{\phi_i-\phi_j}{\rho}}$ is a harmonic function of the form $e^{-in\phi_i}$, and therefore it's eigenvalues are one of the Fourier components of $(|\phi_i-\phi_j|)$. My ...
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0answers
42 views

How does correlation work in an image?

The discrete function for correlation over 2 dimensions is $$ C(x,y) = \sum\limits_{p=1}^{x_{res}} \sum\limits_{q=1}^{y_{res}} f(p,q)h(p+x, q+y)$$ where x,y is a coordinate in the image, f is the ...
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1answer
498 views

explanation of correlation of stationary stochastic processes

I have some doubts about correlation in stationary stochastic processes. I know that the expectation of a random variable is $$E(x)=\int_{-\infty}^{+\infty} a f_x(...
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1answer
1k views

Correlation using fft and xcorr and plot both answers (Matlab) [closed]

I am trying to calculate autocorrelation using fft and xcorr and plot the grafhic with both cases. ...
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0answers
1k views

Triple correlation in MATLAB

How can I calculate a triple correlation between 3 signals A,B,C (each has 2 million samples)? I know xcorr do it for 2 signals by FFT each signal, multiplication and iFFT back. Since xcorr cannot do ...
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1answer
880 views

Echo cancelling using autocorrelation function

I was given a problem, but I couldn't solve. I did some researches but I still didn't figure it out. Here is the problem: An audio signal $ s(t) $ is generated by a speaker reflects in a wall with ...
4
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2answers
3k views

How to measure the time dependent correlation of two signals

I have two signals (time series) shown in the plot below. Just by looking at the figure, we can see that the two main peaks of both signals are very closely aligned (correlated), however the red ...
9
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1answer
7k views

Auto Correlation vs Cross Correlation vs Convolution and their applications

I know from wikipedia that auto correlation in done on the same signal while cross correlation is done on different signals.But what does this actually imply in terms of application.I can always apply ...
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1answer
383 views

Finding Correlation response in fourier domain

Lets say I have a system that is trying to find a small image (assume all images are grayscale) within in an image by using correlation. So this system has the baseline image, and I input 5 different ...
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2answers
174 views

PSD and $\lim_{T\rightarrow \infty} \frac 1 {2T} \int_{-T}^T x(t)\bar y(t)\,dt$

From Wikipedia, I taken a definition of power spectral density: For continued signals that describe, for example, stationary physical processes, it makes more sense to define a power spectral density ...