# Questions tagged [autocorrelation]

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

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### Negative bias in sample auto-correlation of uncorrelated time-series

I am using the following definition for the sample auto-correlation: $AC_x(l)=∑_{i=1}^{N-l}(x_i-μ)(x_{i+l}-μ)$ ; $μ=\frac{1}{N}∑_{i=1}^Nx_i$ I have noticed that this definition introduce a ...
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### 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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### Power spectral density of surface roughness

I am currently working on understanding how visually and intuitively the power spectral density is the fourier transform of the autocorrelation of a signal. I was wondering if anyone had a good ...
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### estimation of ARMA(1,1) with MA parameter greater than 1

I am working with the following simple ARMA(1,1) model: $$z_{t+1} = \phi z_{t} + \theta\varepsilon_{t} + \varepsilon_{t+1}$$ In my case $\theta$ depends on some other parameters, and, therefore, I ...
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### Impulsive autocorrelation sequence

I am looking for a proof that a finite length sequence can only have an impulsive autocorrelation sequence if the sequence is a single impulse itself, ie.: assume $s[n]$ is nonzero for $n=0,1,2,3$ ...
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### What is the autocorrelation of a Dirac pulse?

What is the autocorrelation of $x(t) = \delta(t)$? Can you explain to me how to calculate it?
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### Effect of filtering on Energy of a Digital Signal

I am trying to detect (not remove) noise from the digital signal to get meaningful information out of it. The signal I need is in the frequency range of 0.1 Hz to 10 Hz. Anything beyond this is just ...
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### How to compute the energy of a NON-STATIONARY (transient) random discrete-time signal

When computing the energy of a NON-STATIONARY (transient) random discrete-time signal $x(n)$, does it make more sense to compute the energy as $E=\sum_1^N{x^2(n)}$ over all the $N$ samples or does ...
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### What is the meaning of **Sample** in **Sample ACF**

What is the meaning of Sample in Sample ACF (autocorrelation function)
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### Definitions of PSD, ESD and Autocorrelation

This question is going to encompass multiple areas and may not have a single answer but here it goes. I'm trying to conceptualize 3 different concepts and how they relate to each other. These 3 ...
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### Autocorrelation of a uniform random process

i am currently learning the basics of signal processing. As you may know the definition of the autocorrelation is different if you look at a random process or for example a deterministic signal My ...
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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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### 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 ...