# Questions tagged [autocorrelation]

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

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### What's the relation between frequency band of $X(j\omega)$ and $\Phi_{xx}(j\omega)$?

in which: $x_{c}(t)$ is a continuous-time signal $X(j\Omega)$ is the Fourier Transform of $x_{c}(t)$ $\Phi_{xx}(j\Omega)$ is the Power Spectrum Density of $x_{c}(t)$ which defined as Fourier ...
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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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### aperiodic auto correlation properties

I'm reading about PSC (primary synchronization code) in UMTS. It is a so-called Golay sequence. It is said it has a good aperiodic auto correlation properties. What does it mean (in terms of aperiodic)...
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### Welch's method, no windowing function

I'm trying to pick a method to increase the bin-width on several discrete Fourier transforms I'm incorporating into some scientific analysis code. I have several questions about how this could work ...
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### Autocorrelation not as expected

I am trying to find the autocorrelation function on the intensity of a pixel over time stored in an array "Intensity". Usually one would expect the highest point to be at t = 0 and then decay. I am ...
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### Error in measuring wavelength/frequency using autocorrelation

I am currently using these two fonctions to compute to autocorrelation of a signal in order to measure the wavelength: ...
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### Mean of input based on acf of filtered output

By looking at the ACF of the output of a filter whose impulse response I know, can I approximate the mean of the input? For example ...
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### Autocorrelation of LTI system output

I'm having trouble showing the following relation: The autocorrelation of a LTI system with impulse response $h[n]$, input $x[n]$ and output $y[n]=h[n]*x[n]$ is given as: $r_{yy} = r_{hh}*r_{xx}$ ...
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### ACF of $X_t = a + bt$
I was able to prove the following convergence results. But how can we determine the theoretical autocorrelation function of the deterministic sequence $X_t = a + bt$ and $X_t = c\ \text{cos}(\omega t)$...
I am trying to simulate a simple stochastic process defined by the equation: $$\frac{1}{v}\frac{db}{dt} +\Gamma_0 b= \sqrt{\sigma}R(t),$$ where $R(t)$ is a zero-mean white ...