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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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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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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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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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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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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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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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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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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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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48 views

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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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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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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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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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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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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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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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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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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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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576 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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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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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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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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52 views

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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115 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, ...
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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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Solving nonlinear Fourier relation

I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$: $S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$ with $n&...
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Dependence of correlation peak height on GPS C/A signal's SNR, noise floor level (dBFS), correlation period length and ADC resolution

Assuming correlation at 2X the chip rate (2046 chips per period) and 500 Hz frequency search bins. There are probably additional variables here that I'm missing and I'm not sure how to quantify a ...
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Detect orthogonal sequence with fading

For a set of $N$ orthogonal sequences $\textbf{A}^i = \{a_1^i,a_2^i,...,a_M^i\}, i =1 ..N$, the detection of these sequences can be done by calculating the inner product (dot product) of receive ...
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What is the explanation for the inverse FFT of a cross-correlated signal being shifted by some amount in the time domain?

I created two signals in the time domain: signal A which is a square wave, and signal B which is a right-angled triangle wave, as shown in the picture below. I took the FFT of these signals, ...
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616 views

convolution vs correlation? [duplicate]

What is difference between convolution and correlation?In simple words or in a nut shell? As far as i am able to study is that Convolution is a mathematical operation used to express the relation ...
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107 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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65 views

How to verify if my cross-correlation algorithm works?

So I have a signal generator which can produce two separate signals. I use a spectrum analyzer to read these signals, and can interface with Python. I wrote a Python code which takes in these two ...
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How to extract information about each constituent 'wave' of a signal?

I have a vector containing wind speeds sampled at 1Hz over ten minutes. I have applied a lowpass filter of 0.25Hz to get only the wind speeds I am interested in. I now want to use MATLAB to ...
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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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447 views

What is the time reversal convolution

Given a signal $r(t)$ which is a result of convolution between signal $x(t)$ and a channel $h(t)$ as below : $r(t) = h(t)*x(t); $ what I know, the time reversal convolution can be process as ...
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Pearson correlation coefficient vs mutual information

I recently computed both the pearson coefficient and the mutual information of two time series as well as the corresponding error bars, and what I find out in the end is a significant level of ...
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Are there methods to measure how the change in one signal will affect another signal?

I have two distinct signals and I would like to compute their correlation. However, I think that just computing the crosscorrelation does not work here, since the signals are from different sources — ...
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Find repeating sequences in audio file

I have a long audio file (12+ hours). I know that there are some unknown small (2 minutes each or thereabout, it varies) repeating (not bit by bit: it is recorded with a mic) chunks in it, repeating ...
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86 views

Practical question about DFT in Matlab

Please consider this piece of code: ...