# Questions tagged [autocorrelation]

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

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### Particular Correlation formula

I'm reading a book where the autocorrelation of white noise is expressed as: What is the term $Q(k)$ and why is is expressed as an average value of a dot product ?
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### Difference between autocorrelations

M. H. Hayes calls in his book "Statistical digital signal processing" autocorrelation sequences $r[k]$. For optimal filters the desired autocorrelation has the index d -> $r_d[k]$. However, often ...
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### Correlation between 2 signals of uneven dimensions

As a part of my work, I am trying to correlate the audio signal in a video with the pixels of each frame. The steps I follow are: Audio sampling rate and frame rate of the video are known. So, ...
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### Simulate time series given temporal auto-correlation functions

Given a random process $x[n] \in \mathbb{R}$ (say of length $N$) and all correlation functions such as: \begin{align} \langle x[i]\rangle\\ \langle x[i]x[j]\rangle\\ \langle x[i]x[j]x[k]\rangle\\ \...
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### Confusion about ensembles and averages in autocorrelation matrices

I just noticed that until now I often don't cared about the scaling of the autocorrelation Matrix in Matlab. I then checked with the book Statistical Digital Signal Processing from M. H. Hayes. There ...
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### Autocorrelation

What is autocorrelation in real life? Any example? How does autocorrelation dependent on time difference? Here is Xt1 and Xt2 how comes \phi{tau}?
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### Autocorrelation: numpy versus FFT

I have a series a of values (0 and 1) coming from a Brownian process with drift for which I am studying the autocorrelation. I used two methods: 1) numpy autocorrelation: ...
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### 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 ...
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### 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 ...
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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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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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, ...
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Given a random signal $Z \left( t \right)$ which is addition of two independent signals $X \left( t \right)$ and $Y \left( t \right)$ with constant parameters $a$ and $b$: $$Z (t) = aX(t) +... 2answers 419 views ### Ornstein Uhlenbeck with drift The Ornstein-Uhlenbeck (OU) process dX_t = -\frac{1}{\mu} X_t + \sqrt{\frac{2\sigma^2}{\mu}} dW_t  generates coloured noise with autocorrelation function R(t) = \langle X_t,X_{t'}\rangle = \... 2answers 275 views ### Harmonics to Noise Ratio Estimation I'm willing to estimate the Harmonics to Noise Ratio (HNR) of a speech signal x[k] and using autocorrelation method. Theoretically, HNR is given as, \ HNR = \frac{R_{xx}[T_0] }{R_{xx}-R_{xx}[... 2answers 150 views ### Interpreting this plot cross-correlation I have an input signal x(t) that is a white Gaussian random signal with mean 0 and variance 1. The signal y(t) is the output of a linear filter with impulse response$$h(t) = |\operatorname{sinc}(...
With a delay $l$, autocorrelation is defined as: $$r_{xx}(l) = \sum_{n=-\infty}^{\infty}x(n)x(n-l) = \sum_{n=-\infty}^{\infty}x(n)x(n+l).$$ I want to calculate the autocorrelation of a signal x(n)...
Given two signals $f_1(t),f_2(t+dt)$ where $t$ is time and $dt$ is the time delay between the two signals, is there any closed-form solution with respect to $dt$? what are the efficient global ...