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# Questions tagged [autocorrelation]

Autocorrelation is the cross-correlation of a signal with itself.

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Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal? If I have a measured signal which has good ...
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### Finding period of a square wave with varying sampling frequency

I have a square wave (0-1.8V) with a varying sampling frequency (from a circuit simulator). It is also not a perfect square wave (the high and low signal could be very close to but not precisely zero ...
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### Is there an algorithm for computing auto-correlation in a frame-based manner?

I am trying to find out if an algorithm similar to the Overlap-And-Add method that enables frame-based computation of convolution and cross-correlation exists. When I say frame-based computation I am ...
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### Pitch detection, YIN, pYIN

So here is the "seminal" YIN paper: Cheveigne A, Kawahara H. - YIN, a fundamental frequency estimator for speech and music and the new, improved probabilistic YIN: Mauch M, Dixon S. - PYIN: A ...
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### Interpreting Auto correlation results

I used xcorr function in Matlab to compute the autocorrelation of my signal. I obtained a graph, which is shown below. How to interpret this? I read that autocorrelation helps in finding the patterns ...
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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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### Can spectral density be a complex quantity?

I have a signal ($S(t)$) which is product of a Gaussian ($G(t)$) and a random phase function ($e^{i\theta(t)}$, here $\theta(t)$ is a random function), as shown below $S(t)=G(t).e^{i\theta(t)}$ If I ...
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### How to deduce the shape of autocorrelation graphically?

I'm asking for your help in understanding if I have a rectangular function, so the autocorrelation for it will be triangular... and I can prove that graphically but this is time-consuming especially ...
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(Question already asked on Math StackExchange) Let's say we have a white noise process $x(t)$ such that: $E(X(t)X(t+\tau))=N\delta(\tau)$ $E(X(t))=0$ In particular, with $\tau=0$, $E(X(t)X(t))=E(X^... 1answer 35 views ### Practical insightful time domain functions [closed] This question might be a little bit different, but i am having hard time to find some sort of a list/book/website/advice, with very practical time domain functions that provides useful insgihts for a ... 1answer 76 views ### What does a star shaped autocorrelogram mean? Using the data in the upper graph, I get the weird autocorrelogram of the lower graph:- I've never seen a autocorrelogram of this shape. They're usually flat along the x axis. Testing the code with ... 2answers 124 views ### 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 $$R_{XY}(\tau) = \int_{-\infty}^{+\infty} x(t)... 1answer 15 views ### How can faux correlated data be generated for testing or training? There are one or two questions here that ask how to assess data correlation. The data tends to be empirical. Is there some tool or standardised technique for generating correlated data from scratch? ... 2answers 116 views ### Interpolation of missing audio signal in a video sequence Suppose there is a video sequence and there are some frames for which the audio data is missing. I want to interpolate the missing audio data on the basis of the correlation of the audio signal with ... 1answer 319 views ### How to determine fundamental frequencies (beats/minute) of heartbeat? (matlab) read = matfile('ECG.mat'); [cor, lags] = xcorr(read.ecg, read.ecg); read.Fs; So i have read.ecg (signal) and ... 1answer 35 views ### Why is the sound field intensity due to K point sources given by I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)? I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula (*) below. Statement: 1. We ... 1answer 377 views ### Problem understanding the Expectation Operator I know that the Expectation Operator E\{x\} four discrete values is$$ \sum_k \alpha Pr(x = \alpha_k)$$and its very intuitive when speaking out a formula which contains the Expectation Operator. ... 2answers 607 views ### How to compute autocorrelation of signal defined by difference equations? I have no experience with difference equations and I want to learn how to compute the following, but I found no resource online. Any help would be greatly appreciated. Find:$$\mathbb{E}\left[d[n]d[... 1answer 292 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 ... 0answers 144 views ### How to visualize the autocorrelation matrix and it's properties Having a hard time wrapping my head around autocorrelation matrix as it applies to a spectral estimation problem like MUSIC or ESPRIT. If the signal vector contains a summation of sinusoids in noise, ... 2answers 83 views ### Fluctuation of autocorrelation of a signal due to signal's noise I have a question about the fluctuation of autocorrelation of a signal due to signal's noise. I have a signal defined in$-1\leq t \leq 1$as the following:$V(t)=kt+R(t)$, where$R(t)$is the random ... 1answer 53 views ### Question on Levinson's proposed discrete form of Wiener filter The whole foundation of Levinson's discrete version of Wiener filter is based on the assumption of stationarity of a time series, and aims to predict a value based on the past observed values. Now, if ... 2answers 99 views ### Finding the auto-correlation sequence$r_{xx}[k]$for an AR(2) process Consider the following recursive difference equation of a LTI system, where$v[n]$is a white noise, zero-mean process with$\sigma_v^2 = 1$.$ x[n] = v[n] + 0.75x[n-1]-0.25x[n-2] $I want to ... 1answer 781 views ### Confusion about PSD and RMS Let's say I have a noise power-spectral-density (PSD) which is not flat and ranges from 0 to$f_1$Hz in frequency. As we know, the total area under the PSD is equal to the total average power of the ... 2answers 2k views ### Does the auto-correlation function of stationary random process always converge? The auto-correlation function of the stationary random process only depends on the time difference$\tau$. http://web.ntpu.edu.tw/~yshan/chapter6_han.pdf 64th slide of this lecture note mentions ... 1answer 537 views ### Wiener Filter in Frequency Domain: What it does to a specific Frequency? As I understand Wiener filter in time domain tries to estimate a signal as close as possible to its (original) non-degraded signal using the degraded signal by white noise. $$H(\omega)=\frac{\Phi_{... 1answer 439 views ### While finding the ESD/PSD of a signal why we always prefer to find it via Auto-correlation function then the square of the FT of the signal? [closed] In a video i saw that while calculating ESD or PSD of a signal time auto correlation function was used when it can be also done by the square of FT of the signal.Why we followed that approach even ... 2answers 104 views ### Image Interpolation Using the Yule Walker Equations I have been studying about the Yule-Walker equations for prediction of a time series data from knowledge of past values of the series. Is there any way I can use the same in an image to exploit the ... 1answer 27 views ### detection of periodicities in n-dimensional signals Generally speaking, what analyses are necessary and sufficient for the detection of periodicities in an n-dimensional signal amounting to a discretely sampled density distribution over n-dimensional ... 2answers 305 views ### Why use \chi^2 test to determine the presence of white noise? I want to test for the presence of broadband noise in a snapshot 1000 complex baseband samples recorded by a software defined radio. As a follow-up to this post, why was the \chi^2 test used? How ... 1answer 606 views ### Linear Predictive coding vs AR modeling I'm looking for a suitable explanation of the circumstances in which the LPC error polynomial for a discrete time process x[n] is replaceable with an error polynomial categorized under the AR model? I ... 1answer 938 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 ... 0answers 124 views ### Subtracting audio signal emitted - trying to use spectral subtraction to localize moving objects I am a Software Engineer without much signal processing background and currently spending and experimenting to get use to it. My scenario: Assume a speaker and a microphone array. A speaker emits an ... 1answer 187 views ### What exactly does compression say about correlation of data? I've been using the following formula on various empirical data d, to obtain a correlation factor c_f:-$$ c_f = { |C(d_s)| \over |C(d)|} $$where C is a compression function like bz2 or zip, ... 1answer 64 views ### Auto-correlation of the sum of two generic signals Be x[n] and y[n] two generic discrete-time signals. Given s[n] = x[n] + y[n] I want to evaluate its autocorrelation R_s[l]. By definition (https://en.wikipedia.org/wiki/Cross-correlation):$$... 3answers 293 views ### The explanation of$|R_{XY}(\tau)| \le \sqrt{R_{XX}(0)R_{YY}(0)}$If i said the explanation of$|R_{XX}(\tau)| \le R_{XX}(0)$is that in the time domain,any signal wave are the same as itself when it doesn't shift.Then what is the explanation of$|R_{XY}(\tau)| \le ...
I can show that a process $X(t)$ is Wide Sense stationary (WSS) by showing that $E[X(t)]$ is constant and that its autocorrelation function is in function of $\tau=t_1-t_2$, that is, \$R_X(t+\tau,t)=...