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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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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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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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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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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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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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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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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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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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:
$$C=\left[
\begin{array}{}
a& ace^{-\frac{|\phi_1-\phi_2|}{2}}\\
ace^{-\frac{|\phi_1-\phi_2|}{2}} &...
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How do I calculate the eigenvalues of a covariance matrix which contains harmonic functions
I have read that $ce^{-\frac{\phi_i-\phi_j}{\rho}}$ is a harmonic function of the form $e^{-in\phi_i}$, and therefore it's eigenvalues are one of the Fourier components of $(|\phi_i-\phi_j|)$.
My ...
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How does correlation work in an image?
The discrete function for correlation over 2 dimensions is
$$ C(x,y) = \sum\limits_{p=1}^{x_{res}} \sum\limits_{q=1}^{y_{res}} f(p,q)h(p+x, q+y)$$
where x,y is a coordinate in the image, f is the ...
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explanation of correlation of stationary stochastic processes
I have some doubts about correlation in stationary stochastic processes.
I know that the expectation of a random variable is
$$E(x)=\int_{-\infty}^{+\infty} a f_x(...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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)\ \...
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Timing synchronization in limited channel
I need measure timing of an signal that is send through a noise band limited channel (wireless).
By measure timing, I mean measure as exactly as possible when the signal has arrived at the receiver.
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What Does It Mean Exactly When Two Parts of a Signal Are Correlated?
I stumble quite often upon the notion that two or more parts of a signal are correlated to describe semi-formally that they belong together. For example in image processing, two pixels on an edge ...
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Correlation meter
I have three questions regarding the correlation meters used in audio.
How are they calculated? I have heard correlation is performed by convolving one signal with the time flipped version of a other,...
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What is obtained from the cross correlation plot?
Let’s assume that we have two audio signals, x(t) and y(t) affected by the noise as shown below.
And we would like to cross-correlate these two signals and the cross-correlation plot is shown as ...
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calculate relative error of two signals [duplicate]
I'm new to dsp.stackexchange and digital signal processing. I'm required to develop an app to measure the similarity of two signals.for an example I need to compare breathing of a man whether it is ...
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Minimum Samples Per Chip?
Is there a 'Nyquist Criteria' for the minimum samples per chip that are needed for a correlator? I've heard 2, but will 1 work? What are the implications of having less than the minimum (in the ...
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What type of correlation is this equation?
In a book [1], gives an equation (equation 5.31 in the book) for estimating frequency offset in OFDM systems proposed by Classen. the procedure is:
first, two OFDM symbols, $y_l [n]$ and $y_{l+D} [...
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Autocorrelation function of a discrete signal
For a certain experiment of which I have data, I want to calculate the autocorrelation of the measurements. For this I used the expression from Wikipedia, which reads
Here, $n$ is the dataset's size, ...
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Extracting common signal from 4 sets of observations
I am working on a signal processing assignment where I need to find out one common time domain signal from 4 observation. The math is like this:
\begin{array}{lcl} y_1(t) & = & a_1(t)*x(t) + ...
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Finding correct values based on information from two arrays
Consider the following scenario:
Say, one machine is sending out a beep signal every 10 seconds in a very noisy environment. I have two sensors which detects these beeps independently. Device A is ...
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Using a Wiener Filter to Estimate a Transfer Function
As a follow on Estimate the Transfer Function of an Unknown System which os estimating a transfer function of an unknown system using a Wiener filter,
How would you put a minimum MSE criteria on how ...
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