# Tag Info

### Covariance vs Autocorrelation

According to your definition of autocorrelation, the autocorrelation is simply the covariance of the two random variables $Z(n)$ and $Z(n+\tau)$. This function is also called autocovariance. As an ...
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### Why do we need to conjugate complex signals in autocorrelation and cross correlation

$\underline{\text{Prologue :}}$ Let me ask you another question. How will you compare two complex numbers $U$ ($a+jb$) and $V$ ($c+jd$)? By comparing magnitude? Subtract them and take real part? ...
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### What is the difference between convolution and cross-correlation?

As a student I was involved in the same problem as you are. Let me explain to you in the simplest words without any math. Convolution: It is used to convolve two functions. May sound redundant but I'...
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### Estimating period of low frequency oscillations: autocorrelation vs. Frequency approaches

Similar approach to Dan's but a different way to go about it. First lets define what exactly we mean by "peak" frequency. I suggest it is the frequency that minimizes the square error ...
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### When is it true that "the Fourier transform of the autocorrelation is the spectral density"?

The magnitude-square $\Big| X(\omega) \Big|^2$ of the Fourier Transform of energy signals is the energy spectral density. For power signals, you gotta do a little bit with normalization, so that ...
Accepted

### Confusion about ensembles and averages in autocorrelation matrices

First, the output of the xcorr() function returns lag-0 of the auto-correlation sequence (ACS) estimate at its middle sample, as you recognize. The function argument scaleopt provides normalization ...
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### Allan Variance vs Autocorrelation - Advantages

My current work involves the design details of atomic clocks where we use the Allan Variance and Allan Deviation (ADEV) extensively. The primary point is that it can be used for non-stationary ...
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### Estimating period of low frequency oscillations: autocorrelation vs. Frequency approaches

I'd just add to these two fantastic answers that since the frequencies of interest are so low compared to your sampling frequency, I imagine you can also decimate your signal quite a bit before trying ...
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### AutoCorrelation Matrix vs Covariance Matrix for the MUSIC Algorithm

That really depends on who is asking and precisely what definitions you want to use. In signal processing, the autocovariance is usually a non-normalized, mean-corrected quantity derived from a ...
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### How is the energy of $x_1\cdot x_2$ related to the energies of $x_1$ and $x_2$?

Knowing the energies of $x_1$ and $x_2$ is not sufficient for determining the energy of $x_3=x_1x_2$. What you can do is determine an upper bound for the energy of $x_3$ given the energies of $x_1$ ...
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### How to prove that the peak of the autocorrelation function is at zero lag?

The Cauchy Schwarz inequality states that: $$\left|\int_{-\infty}^{\infty}g_1(t)g_2(t) dt\right|^2 \leq \int_{-\infty}^{\infty}|g_1(t)|^2 dt \int_{-\infty}^{\infty}|g_2(t)|^2 dt$$ I'm going to ...
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### How to estimate the autocorrelation from nonuniformly spaced data

As suggested by Marcus MÃ¼ller, interpolation in the time domain could be a solution. I never had to perform such a task, and the outcomes may depend in the nonuniformity of your sampling. I propose a ...
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### Power spectral density of $\left(x(t)\right)^2$?

Since the question has been raised as to whether the hint that I had given to the OP in a comment on the original question was appropriate for a newcomer to signal processing, here goes. Stripped of ...
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### How can define an indicator which measures the degree of similarity between two signals?

The general topic of finding similarities between signals is wide ranging: are the signals of same sampling, length, offset, shift or scale? where do they take their values (discrete, real, complex)?...
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### Relationship between the autocorrelations of X(t) and X(nt)

The answer to the OP's question is more straightforward than rb-j's comments make it out to be. $\{X(t)\colon -\infty < t < \infty\}$ is a continuous-time WSS random process with ...
• 20.5k
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### Autoconvolution vs Autocorrelation

Are two signals are the same if their auto-convolution functions are the same? Not quite. Look at the autoconvolution in the frequency domain where the ...
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### Why autocorrelation can be more efficiently calculated using the fft

The cross-correlation between two functions $f(t)$ and $g(t)$ can be seen as a convolution of $f(t)$ and $g(-t)$. The auto-correlation is of course a special case where $f=g$. This operation in the ...
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The derivative of the Dirac delta impulse is written as $\delta'(\tau)$. This helps with notation because the mistake you made is to write $h(-\tau)=\frac{d}{d\tau}\delta(-\tau)$, which is not the ...