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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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
144 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
225 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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1answer
7k 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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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
63 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
100 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
980 views

Tied rank adjustment for Spearman Correlation

I have two 16 sample vectors, a and b as listed below: ...
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1answer
2k 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
360 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
675 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
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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
106 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
193 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
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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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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
270 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
851 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
57 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
341 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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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
411 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
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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
984 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
781 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 ...
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2answers
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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 ...
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1answer
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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
314 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
165 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 ...
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1answer
180 views

Power Spectrum Analysis

In order to find a peak or max response in the fourier domain as in the spatial domain, I have been studying bartlett's method, welch's method, and the blackman-tukey method for more accurate power ...
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1answer
501 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 ...
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510 views

Correlation between two graphs in Matlab

I am trying to make a system that detects footsteps. First I filter and decimate the original signal, then I make a convolution between the filtered signal and a single footstep, then I extract the ...
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1answer
119 views

Can we decompose a correlated random variable into correlated plus uncorrelated?

Assume a random sequence $ Y_k = X_k \cdot H_k + W_k $ where $X_k$ is a deterministic quantity, $H_k$ is a correlated random sequence, $W_k$ is Additive White Gaussian random sequence. Can we ...
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5answers
712 views

Looking for an algorithm that computes “Similarity” between two signals

I'm new in this forum! ... and I'm not an expert in signal processing! ... So I hope to find help here:-) I was wondering if someone could point me to an algorithm/technique that is used to compare ...
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2answers
100 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 ...
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1answer
159 views

What is spatial correlation?

What does the spatial correlation of a signal say about it?How is it different from autocorrelation? `
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0answers
88 views

Measuring typical seperation between patches using 2D Fourier Transform

I need to extract information about the typical distance between the black patches in an image like the one I attached here. Typical distance would be the the most frequent separation between two ...
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1answer
270 views

Image registration / fusion optimal similarity metrics

I have a theoretical question about optimal similarity metrics for comparing data sets. In reading this linked paper, pp. 488-489 [1], I read the following 2 interesting statements. On page 488: ...
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0answers
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improve delay detection between two signals

Hi there I'm trying to measure time delay of one percussive event recorded by two contact mikes on a glass surface. I decided to check the cross correlation (via FFT) and detect the index of the max ...
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1answer
330 views

Problems filtering image with prewitt

I'm trying to filter an image vertically to get the edges, in MATLAB, but I get very different results from convultion and correlation. CODE: ...
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6answers
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Find Short Clip of Audio Within Longer Clip Of Audio

I need help figuring out a way to automatically synchronize two audio files that are both different recordings of the same source. More info below. This example is from a concert, where there is only ...
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1answer
2k views

Correlation between Sin and Square wave

I would like to know how $\frac T2$ came for time period in the image below.Because I think the frequncy is 1 so time period should be 1.Is that correct? or can anyone help me.. The article from ...
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4answers
675 views

Similarity between two Signals: cycle by cycle

I need to find the similarity between two signals, i.e., measured signal and the reference signal(e.g. a simple sinusoidal signal). What I mean by similarity is, if there is any decentralized glitch ...
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1answer
136 views

Image correlation confidence measure

I am trying to calculate the disparity between stereo image pairs. I'm using what appears to be the standard approach of correlating between a window of pixels from one image and a sliding window ...
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0answers
851 views

Why does a phase shift in the frequency domain not produce a time delay in the time domain?

Suppose I have an input signal which represents a vehicle front suspension response that has been measured using an accelerometer. It is seen that the measured rear suspension response is effectively ...
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1answer
524 views

Measuring the similarity of two waveforms [closed]

I have two approximately sine truncated waveforms of different amplitudes and I want a numerical measure of how similar they are to each other. I am sending a sonic pulse train whose multiple ...
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1answer
1k views

Cross-Correlation : Comparing two signals or finding the location of a target

I read across places that cross-correlation of two signal (a radar sending a signal and receiving it back) one can detect the location (distance) of a target from a point and that cross-correlation ...
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1answer
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Correlation : Cross correlation why we need to multiply the samples

I understand what books states about cross-correlation of signals and their mathematical representation: For continuous functions f and g, the cross-correlation is defined as: $(f \star g)(\tau)\ \...