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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1answer
39k views

Difference between correlation and convolution on an image?

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 ...
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3answers
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 ...
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2answers
689 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 ...
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2answers
7k 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 (...
9
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2answers
2k views

Is a wavelet-based correlation measure worth any additional computational overhead?

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 ...
9
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1answer
6k 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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3answers
8k 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 ...
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2answers
5k 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). ...
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1answer
1k views

Ambiguous results of phase correlation in pattern recognition

We are using phase correlation to find pattern on image and what we get is 15% of results is spurious. Ours pattern has 32x32 pixels and image for research has 32x512 pixels. So we put Pattern to ...
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1answer
652 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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1answer
1k views

Correlation filter output range normalization

I'm developing correlation filters based image recognition. I implemented MACE correlation filter in matlab: training code: ...
5
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1answer
435 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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1answer
17k views

Cross correlation with FFT and fftshift

When I calculate the cross correlation between two vectors with the following code ...
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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
223 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 ...
4
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2answers
148 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 ...
4
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1answer
3k 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 ...
4
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1answer
2k views

Matching masked images

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 ...
4
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1answer
249 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 ...
4
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1answer
88 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 ...
4
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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 ...
4
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1answer
265 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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6answers
1k 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 ...
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4answers
82 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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2answers
2k 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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2answers
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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 ...
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1answer
316 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 ...
3
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2answers
12k 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 ...
3
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1answer
143 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 ...
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2answers
2k 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 ...
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2answers
2k 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): ...
3
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1answer
133 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) + ...
3
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1answer
355 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 ...
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2answers
994 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: ...
3
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0answers
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 ...
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1answer
122 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?
2
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1answer
104 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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2answers
464 views

Need help understanding convolution indexing

Ok, this is leaving me increasingly frustrated. This builds on a previous question here but I am still not getting the indexing, although I learned from that question all the same. Case 1: First ...
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1answer
1k 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 ...
2
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1answer
334 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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2answers
582 views

minimum sampling rate for very short duration signals

I understand that sampling rate should be twice the signal bandwidth for successful reconstruction. But what I don't get is how this translates in the time domain. For example, I have a sine wave ...
2
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1answer
269 views

Designing an efficient curve-matching algorithm

I'm currently designing a curve-matching algorithm and as I already explored many ideas I'm requesting your help. So, if you got some advices about how to handle this problem, feel free to answer! ...
2
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1answer
322 views

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,...
2
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1answer
523 views

Cross-correlation of time compressed 1D signal

If I ave 2 otherwise identical 1D signals that are phase shifted from each other then cross-correlation is a perfect way to identify the time lag between the 2 signals. Now supposing I double the ...
2
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1answer
65 views

What is the set of most predictable or in other words most self-correlated signals?

Which signals or set of signals is the most predictable or in other words most self-correlated (autocorrelation)? I think one of them is $x(t)=c$, for all $t$, where $c$ is a scalar constant. The ...
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1answer
684 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
3k 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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2answers
1k views

MACE correlation filter - any suggested values of of u?

I am trying to understand the MACE correlation filter as per the paper Mahalanobis, A., Kumar, B.V.K.V., Casasent, D.: Minimum average correlation energy filters. Appl. Opt. 26, 3630–3633 (1987) ...
2
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1answer
85 views

What kind of power spectrum implies uncorrelation in time?

I am new in signal processing field, and actually I just need some basic tools for what I am working on. I've learnt that the autocorrelation function is the inverse Fourier transform of the signal's ...
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2answers
321 views

How can I synchronize signal from an LED and TTL pulses better?

I would like to synchronize my video and voltage data using Python. (I obtain these data using Bonsai and Open Ephys for an open field exploration experiment.) I sent $150\text{ ms}$ long TTL pulses ...