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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 of vector signal

This is probably more of a mathematical question than a signal processing exclusive, but I hope somebody here knows an answer! I want to compute the autocorrelation of a signal, which is a vector (so ...
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Aperiodic Correlation function using FFT Method

Periodic correlation function between two binary sequences say x and y can be computed using FFT. corr_value = ifft(fft(x).*conj(fft(y)); Can some one please help on how to compute aperiodic ...
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PRN code design for satellite navigation system ( A-CDMA systems)

Satellite Navigation Systems are based on CDMA principle(asynchronous CDMA). It is observed that there are lot of PRN codes designed in the literature. The requirements of navigation systems is such ...
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Why is correlation involved? - Axis Rescaling for a 2D axes - brightfield illumination microscopy of blood cells

for 1D axis rescaling, you use a FOV calculation len_pixel=total_magnification * len_specimen_in_pixel len_specimen_in_pixel=len_pixel/total_magnification and then to get the axes rescaled, you do ...
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Time delay estimation of signals increasingly decorrelated

The problem may be summarized as follows: I have a stochastic signals and I want to measure an increasing delay, as depicted in the following picture. The picture represents the signal as it is being ...
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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 ...
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What is the betwwen [i,j] and [u,v] in explinations of correlation and convolution (picture attached)?

I don't know how to write 'summation' symbol here hence posting the picture. Can someone explain to me the difference between i,j and u,v in this explanation of correlation and convolution? I know ...
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Efficient correlation of a low duty cycle training sequence

Is there a way to efficiently correlate a training sequence that is N samples long, framed at M samples where M >> N, with L occurrences of such frames (see below). For the pedants, the training ...
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What is the difference between using corrcoef to compare two signals by column, and as whole matrices?

I have two matrices, which represent acceleration readings of the same event from two seperate sensors, and I would like to calculate the correlation coefficients so that I may get a measure of how ...
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102 views

How to get the background noise of microphone?

I am working on the automatic volume control for television which should take care of background noise. For this, I need to first find out the background noise. I have read in research papers that we ...
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52 views

Detection complex vectors by using correlation

I sent out a complex vector $x_i \in \{x_1,...x_n \}$ and receive a vector $y$. I use correlation $y^Hx_i$ to detect which $i$ was sent. If $y$ is corrupted by AWGN channel, the optimum rule should ...
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Co-prediction of signals

Is there any plausible method to estimate or predict one signal, on the basis of known value of another signal, provided the two signals bear a strong correlation? For instance, the audio amplitude ...
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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 ...
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Two different definitions of cross-correlation

I have come across two different definitions of the cross-correlation function: $$ R_{XY}(\tau) = \int_{-\infty}^{+\infty} x(t) y(t+ \tau) dt $$ and $$ R_{XY}(\tau) = \int_{-\infty}^{+\infty} x(t)...
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How can faux correlated data be generated for testing or training?

There are one or two questions here that ask how to assess data correlation. The data tends to be empirical. Is there some tool or standardised technique for generating correlated data from scratch? ...
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What level of correlation coefficient suggests correlation?

In Python (and Numpy), I recently did:- a = np.random.randint(0,256,1000) b = np.random.randint(0,256,1000) and when I calculate the correlation coefficient $r$ ...
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How to interpret correlation angle from frequency domain

Since the coefficient of one frequency could be seen the length of the signal projects on that frequency basis. And the length is $$|a|\cos\theta= \frac{a\cdot b}{|b|} $$ If I divide the ...
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62 views

Correlation of a signal

I have one sample for a signal. This sample is a vector of length 384. I need to calculate the correlation matrix for this signal,So I need many samples for the same signal. How can i generate these ...
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Confidence measure for GPS CA Code Acquistion

As a follow-on to this question, how do GPS receivers decide if they've successfully acquired the coarse acquisition (CA) code for a GPS satellite? If it's based on post correlation SNR, what's the ...
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78 views

Correlation between slightly misaligned images

I am matching camera images of projection screens with rendered pages of PDF documents using Pearson's and Spearman's correlation coefficient. When the images (3, 4, 5) are aligned, this works fine in ...
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BER performance of fractional equalizers for colored noise

I am trying to compare the BER performance of fractional and symbol spaced equalizers for channel equalization in colored noise scenario. I have found from simulation that for positively correlated ...
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How we can show that 2 correlated videos are similar?

Can I tell that different versions of the same video are correlated to each other? and if so, how can I show this correlation? for example, high-quality and poor-quality versions of the same video. ...
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Positive definites of correlation functions

Say I you have two time series, $x_k, k=1,2$ generated from two, possibly correlated, complex gaussian processes. The lag 0 and 1 auto-correlation estimate for the two time series is denoted $R_{0,k}, ...
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158 views

Matrix cross correlation in python

I'm currently performing matrix cross correlation in python using : C = scipy.signal.correlate2d(A,A) where A is a 2D matrix, typically a picture. As you can ...
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132 views

Correlation peformed by convolution

Background: The question here is related to images in particular and not signal/waveforms. I have been reading a lot of answers about the difference between convolution and correlation but I am stuck ...
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283 views

How can I align these two signals? Cross correlation isn't working properly

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). ...
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139 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 sent $150\text{ ms}$ long TTL pulses to a computer recording the voltage data, at the same time as to an LED in the field of view ...
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80 views

Calculation of Correlation Matrix

In the description of any Beamforming Technique for microphone array signal processing there is a usage of the co-relation matrix. What is the use of calculating such a co-relation matrix in such ...
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Investigating correlation for unequal signal lengths

I have measurements from two tablet sensors. The first sensor measures the touch pressure applied to the tablet and the second sensor is the acceleration of the tablet (in z direction). The sensor ...
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Relationship between signal amplitude and input output correlation

I have a linear system with input $ x(t) $ and output $ y(t)$ given by $$ y(t) = \int_0^\infty K(t')x(t-t')dt', $$ where $K(t)$ is a known kernel, with some parameters. The functional form of $K(t)$ ...
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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! ...
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1answer
318 views

DoA estimation using microphone array

I am using an array of 4 microphones in a square formation. My goal is to estimate the direction (azimuth only) of incoming speech sound. The array looks like this: I have recordings from the array ...
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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?
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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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116 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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423 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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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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679 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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197 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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794 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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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
442 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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194 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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130 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
3k 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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2k 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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258 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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1k 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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132 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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956 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 ...