# Questions tagged [autocorrelation]

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

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### variance in the time domain versus variance in frequency domain

Hi All: I'm trying to better understand the connection between variance of a time series and the integral of the spectral density over all frequencies. Rather than going through all of the relations, ...
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### Definition of average power?

There are two kind of average power I encountered in random signal class and textbook: definition 1: average power =$$E[|x(t)|^2]=R_{xx}(0)=\int^\infty_{-\infty} S_{xx}(f)\,df$$ definition 2: average ...
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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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### Autocorrelation of two dirac pulses

I am given a channel impulse response: $$h(t) = 0.8 \times \delta(t) + 0.6 \times \delta(t - T)$$ where $\delta(t)$ is the dirac function. For signal equalization a MMSE equalizer with 5 ...
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### Finding autocorrelation matrix of an autoregressive process AR(1)

Having that $\ v(n) = [x(n),x(n-1),x(n-2))]^T$, and being $\ x(n)$ an autoregressive process AR(1) with known variance $\ \sigma_v^2$ and transfer function $\ H(z) ={ 1 \over {1-0.7z^-1}}$, how ...
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### Python different autocorrelation with FFT and non-FFT

Im trying to calculate the autocorrelation of soundwaves when I noticed that I get different results with scipys FFT based and with numpys methods. The 4 functions Im using: ...
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### Find autocorrelation of exponential signal $a^nu[n]$

I need to find the autocorrelation of the following discrete signal $$x[n]=a^nu[n]$$ So I tried finding the convolution of $x[n]$ and $x[-n]$. \begin{align} \phi_{xx}[n]&=\sum_{m=-\infty}^\...
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### Estimating confidence intervals for the mean value

Say I conducted a numerical experiment -a time-dependent fluid simulation- and extracted a time-series of some variable. It looks like this: As a result of the simulation, I am supposed to report the ...
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### What kind of filter I should use to remove the oscillations in this autocorrelation function?

I have an autocorrelation function which is shown as following, I do believe these trailing oscillating wigs are spurious and should be removed by some kind of filter. But I am not familiar with any ...
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### Wiener filter yielding negative MSE (and MMSE)

I implement a Wiener filter using the following code ...
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### Covariance vs Autocorrelation

I'm trying to figure out if there is a direct relationship between these concepts. Strictly from the definitions, they appear to be different concepts in general. The more I think about it, however, ...
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### How to calculate autocorrelation function of an image noise

I am trying to calculate the autocorrelation function of an image noise. Specifically, I want to calculate the NCORR parameter in the function deconvwnr(). I have knowledge about the noise, which is ...
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### LTI filtering for wide-sense stationary process

Why is it that if $U[n]$ is wide-sense stationary and it is convolved with $h[n]$ to produce $W[n]$, the autocorrelation becomes $R_{WW}[n] = R_{UU}[n]*h[n]*h[-n]$? I know that in general \$R_{WW}[n_{...