# 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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### Difference Between Correlation and Convolution in the Context of Image Processing

Could you please clearly explain what is the difference between correlation and convolution that is done by a filter on an image? I mean in terms of signal processing definition I know that ...
2k views

### 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 ...
8k views

### Phase Correlation - Poor Performance on Noisy/Blurred Images?

I have successfully tested 1D phase correlation algorithm to determine vertical shift between two synthetic images. When I moved to real images, however, it is not able to detect translation at all (...
2k views

I have used both correlation and coherence as measures of correlation between signals. I was thinking that a time-frequency approach would give me the best of these worlds. My question is whether ...
816 views

### 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 ...
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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### 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?
9k views

### Calculating similarity between two signal plots

I have two plots, each having frequency as x-axis and Gain as y-axis. By taking one data set as a reference I have to calculate similarity between them. The graphs have same values on the x-axis and ...
7k views

### Detection of lines in a point cloud

What are the best solutions to detect line in a point cloud? Comparison being made with and between Hough Transform, Radon Transform, RANSAC (see wikipedia) and Brute-Force Search (see wikipedia). ...
173 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 ...
358 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:...
8k 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 ...
500 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 ...
366 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 ...
1k views

### Time Alignment of 2 Sensors Sampling the Same Signal with Different Hardware Delays

I have two radios sampling simultaneously, and I am trying to time-align their two signals (they will always start sampling at slightly different times with random delays due to hardware differences). ...
868 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 ...
2k views

### 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 ...
1k views

### Correlation filter output range normalization

I'm developing correlation filters based image recognition. I implemented MACE correlation filter in matlab: training code: ...
575 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 ...
19k views

### Cross correlation with FFT and fftshift

When I calculate the cross correlation between two vectors with the following code ...
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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### 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 ...
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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Let's say I have two images that are parts of the same bigger image, cut using two masks (for simplicity, let's assume that the masks are just rectangles of the same size). The images are presumed to ...
263 views

### Matching delayed signals

I have pairs of 1d digitised waveform signals which are almost identical - except there are sections which are the same in both but one is delayed slightly. I need to find sections and the delay with ...
99 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 ...
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 ...
272 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: ...
2k 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 ...
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### Compressive Sensing - Incoherence Property

Compressive Sensing is built on 2 properties: 1) the sparsity of the representation basis relative to the sampling basis and 2) the incoherence between the singular vectors from each of the 2 bases in ...
340 views

### Can FFT Substitute Correlation for This Case?

I'm trying to determine frequency of a repeating pattern in a time series. The sampling rate 100Hz and the pattern repeats itself with periods between 0.5 second and 1.25 second. This corresponds to a ...
210 views

### Applying Circular Cross Correlation in MATLAB

I have searched Google for circular cross correlation using Matlab, and I have found it only for one dimensional signals. Could you please help me implementing circular cross correlation between two ...
482 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(...
13k views

### Applications of Correlation in Signal Processing

There have been discussions on the differences between convolution and correlation, autocorrelation, cross-correlation, et al. In spite of looking at the visualizations, and understanding the formula ...
194 views

### Component of one signal along the another

Whenever we need to find component of one signal along another signal we can do so by the help of dot product. I want to as if this method is valid for all kind of signals. Are there any restrictions ...
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 ...
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 ...
4k views

### What is spatial correlation and spatial convolution?

What does the term spatial correlation and spatial convolution mean with respect to digital image processing ?
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### Correlation: A Magnitude or Power quantity?

I am confused about the units we would refer to with a correlation result in that if it would be a magnitude or power quantity (and therefore specifically when using ratios in dB would we use 10Log or ...
3k views

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

### 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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### Proving that FFT (and by extension any correlation based estimator) is unbiased

I have a pretty simple question which i should have been able to answer. Just wanted to check if people here have a better solution to it. I am trying to establish that FFT as a frequency estimator (...
485 views

### 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 ...
458 views

### How do you find signal similarity when one signal has zero values? Correlation alternative?

I'm using cross-correlation to look for a Barker code in a BPSK signal. It occurred to me that if I send out a zero DC valued signal proceeding the barker code, it won't affect the correlation ...
1k views

### Phase Correlation and Negative Shifts

I am implementing phase correlation algorithm to determine shift between two images. It generally works, but I am not sure how to interpret the resulting shift. Pseudocode: ...
9k 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 ...
91 views

### Identify which of the three signals is closest to a sinusoidal curve

I have some acceleration values from a sensor. These values are reported as x, y and z components of the acceleration. As can be seen in the attached figure, it is clear that the z signal has a clear ...
224 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?