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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Determine reflections from received signal

I have a reference signal $r(t)$ and the correlation between that reference signal and the received signal : $C_{XR}(\tau)$. The signal I receive contains reflections on walls. I have to build a ...
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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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When is the Correlation Coefficient Ergodic

Given Wide Sense Stationary (WSS) processes X and Y that are ergodic to the mean and autocovariance. Under what conditions is the correlation coefficient ergodic to the mean? ie: $lim_{T->\infty} \...
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115 views

Does this make sense for cross-correlation in frequency domain?

If I have a signal A at 2 kHz and signal B mixed at 2 kHz + 3kHz, and then i take the FFT of them both, and then cross-correlate them many times, the 3kHz peak should disappear? Since this peak is not ...
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37 views

Calculating cross-correlation using Walsh-Hadamard transform

I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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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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49 views

Why there is static noise and voice distortion after convolving it with impulse response?

I have been working on the decorrelation of audio signals while following this paper : The Decorrelation of Audio Signals and Its Impact on Spatial Imagery So far I have generated impulse responses in ...
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59 views

high & low pass correlated dither noise question

I read a pretty cool article the other day: Robert Katz - Dither noise Probability Density Explained. It says that if you have two dice (A and B) that you can roll both dice and then... Re-roll die A ...
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Calculate ACF in C++?

I would like to manually reproduce the method that authors of an article used in their research (DOI: 10.1038/s41598-017-02750-9 (Page 8. top)). It is mentioned as "ACF", so I wrote ...
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179 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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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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correlation matrix for complex white noise does not equal to identity matrix?

I generate 8 time series of gaussian white noise and want to compute the correlation matrix at a frequency bin between them. The following is the matlab code I use ...
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autocorrelation of multiple signals

Problem: I am looking at an adaptive filtering application where the eigenvaluespread of the autocorrelation matrix $R$ is important for the convergence of the algorithm. For a single channel system ...
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Can somebody explain SDF and MACE to me?

I can't find any information on SDF and MACE save for a vague exert in Kinser's Image Operators books. Therefore I am dumbfounded. I can't understand what they do and what's their role in composite ...
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62 views

Correlations of matrix

I have a matrix of 10 column, each column has measurements at different times. I have a second matrix also of 10 columns, each consisting of measurements at different times. I want to carry out cross ...
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29 views

Do we assume modulating and carrier signal uncorrelated in AM modulation?

I am new to communication and studying amplitude modulation. Let us assume an amplitude modulated wave given by $$\big(m(t)+ A\big) \cos(2\pi f_c t)$$ Now we have formula for efficiency as $$ \eta=\...
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NaN values with correlation metrics

I am using the Peak to Correlation Energy (PCE) Metric to measure the similarity between two images using MATLAB. In some cases, the PCE value obtained is NaN. How can I solve this problem?
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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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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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Linear correlation of two vectors?

We had a lecture on digital watermark detection using linear correlation. Here it was explained that the linear correlation of two vectors is equal to their scalar product divided by the dimension. So,...
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42 views

Spatial multiplexing MIMO, antenna critical spacing, antenna isolation

How does antenna isolation affect single user spatial multiplexing MIMO performance in an antenna array? Text books talk about a critical antenna spacing of 1/2 of the wavelength provided that the ...
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Couting exact number of mutiplications in Separable filters with Zero Padding

I'm convolving an Image $I$ of dimension $2\times 3$ with a kernel of size $2 \times 2$ and counting the exact number of multiplications.My image and kernel are given as follows $$ I=\left[\begin{...
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Comparing two small audio files (e.g., hand clap) Android

Dears, I am new in signal processing and I am dealing with an Android application that should do some audio files (having the same "small" duration) comparison in real time. My main focus is ...
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Can i increase the SNR of the signal by increasing the processing gain by correlation?

If I am having a 13 bit pattern and sending it at IF frequency on the transmit side. On the receive side after IF conversion I am sending it to ADC. After digitizing the signal and removing the IF by ...
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45 views

How to measure correlation between 1 bit samples and theoretical original waveform?

I'm investigating quantization error. I have an analogue waveform that looks like this and is of theoretically infinite resolution:- I've sampled it as (8 bit oscilloscope readings & 0b1) to ...
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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 ...
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Is there any way to align temporally two signals in spectrogram?

I am keen to know that If I have two signals say : Farend_signal (y[n]) and Nearend_signal (x[n]) and x[n] also contains an echo of y[n] with some delay. Is there any technique to align these two ...
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648 views

Autocorrelation function and correlation integral

I am confused by the definition of autocorrelation function. It is originally defined as the expected value $$R_{XX}(\tau) = E[(X(t)X(t+\tau)] = \langle X(t)X(t+\tau)\rangle\tag{1}$$ where $\langle\...
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Self-correlation vs Digital frequency: figure from paper

In the paper, is discussed a MIMO-OFDM system over the frequency self-correlation of i.i.d. Rayleigh channels and subcarrier grouping. in this paper is shown the following figure. it shows the self-...
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Noise and harmonic elements w/in a discrete time signal

So I have a discrete-time signal with around 300 samples. It is part of an environmental science application, so is not-strictly periodic although there clearly are periodic components. I have applied ...
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nature of output of the addition of white noise with colord noise

I want to know that the addition of a uncorrelated time series x with a correlated time series, say y generates a time series ...
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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 (...
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258 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:...
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Comparing mechanical signals with different length

I couldn't find any solution for this that would work for me I'm working in python. I have two similar signals that I can plot Force x Angle. (problem simplified) One plot (angle x force) has length ...
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How does Correlation for 1D Signals work?

On page 2 of the slide, I don't understand the example. Like $j$ and $s$ are both on the x-axis, what does j+s mean? The filter is $(f(−1), f(0), f(1)) = (−0.5, 0, 0.5)$. How can we use it? Could ...
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Are ACF plots sufficient to detect white noise assuming probable existence of non linear associations?

ACF plots use autocorrelations tests to determine associations in time series. Autocorrelations, however, only measure linear associations. To my understanding, certain non-linear associations can ...
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correlation matrix vs. correlation function?

Can someone help me understand the difference between a 1-dim autocorrelation function and a 2-dim autocorrelation matrix of a random process aka time series? My Leon-Garcia textbook defines CX(τ) and ...
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254 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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packet encoder RF packets by using LPF for determining if it's zero or one [closed]

I'm transmitting RF packets with frequency 868MHZ , symbol rate (it's the same as bit rate) is 50KBaud , and Im sampling them by a dongle (fs=20480KHZ) to capture those RF packets, the captured ...
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Deciding if the received packet is valid or not valid [closed]

I have sampled RF wireless packets as IQ samples file, those RF packets has patterns like preamable|syncword|data|crc , I'm doing cross correlation with my constant syncword (after I did the ...
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Find Syncword (pattern) in signal, using Correlation

I have a signal which always has the same syncword ([93 0b 51 de] in hexa). I also have a signal with additive noise(attacing it, and I want to find my syncword in that a noisy signal using corelation(...
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Correlated fading channel: transmit and receive antenna correlation matrices

I am trying to create a non-i.i.d channel: correlated Rayleigh fading channel. $$ H= R_H \cdot H_o,$$ where $H_o$ is i.i.d. channel ( uncorrelated) and $ R_H$ is a channel correlation matrix, is ...
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argmax of the cross correlation

I want to find the shift between 2 signals $\sin a$ and $\sin b$ where (with Matlab code) $$ a = \{0, 1,2,3,4\} $$ $$ b = a +1 $$ $$ \implies b = \{1,2,3,4,5\} $$ then $$ \arg\max \sin a = 2 $$ and ...
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Correlation of discrete time periodic sequences

So I was reading this textbook - Digital Signal Processing by Proakis and Manolakis. The authors define the cross-correlation operation for 2 energy signals $x(n)$ and $y(n)$ in section 2.6.1 as: $$ ...
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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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Autocorrelation - Understanding reduced correlation at periodic time shifts using np.correlate (versus statistical autocorrelation)?

I'm going through the Think DSP by Allen B. Downey, and I'm struggling to understand a specific aspect of np.correlate and how it differs from statistic autocorrelation. The question is at the bottom, ...
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How to find if the signals are in sync or out of sync with each other?

Considering these are two signals over time, black and red.Following are some of the properties Every Second a new data point is added over time . There is no control on the generation of the ...
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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 ...
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606 views

Detecting a frequency pattern in the frequency domain

I am looking to detect a combination of frequencies in the frequency domain. For example, here is my spectrum: And I'm trying to detect the pilot tone. I have the FFT of the pilot tone: which zoomed ...
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132 views

Kronecker delta instead of dirac delta as correlation function of white noise

From my understanding, if you have a sample $x_{t_1},\dots,x_{t_n}$ of $X_{t_1},\dots,X_{t_n}$ which are iid $N(0,1)$, then $x_{t_1},\dots,x_{t_n}$ is a sample path of Gaussian white noise. However, ...