# Questions tagged [autocorrelation]

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

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### Finding a region where a function is periodic

I am looking for a method to find the region where a function is periodic. So, for example, I have a function that is periodic in some places and not in others, I would want to know the range of x ...
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### Proving a cyclostationary processes signal

Suppose a random signal $x(t)=\sum\limits_{n=-\infty}^\infty Z_n \delta(t-n\tau)$, where $z_n = Z$ and $Z$ is a random variable with equal probability to be $+-1$, is passing through a low pass ...
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### Understanding the definition of mean/autocorrelation

I was studying about the definitions of mean, expected value and autocorrelation. I wanted to verify my understanding the evaluation of mean, expected value and autocorrelation. At the same time to ...
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### Isolate recurrent pattern vs. evolving background sound

Here is a sound example for what follows. Let's assume we have a signal $$s(t) = r(t) + e(t)$$ where: $r(t)$ is a signal which is recurrent with a given period, i.e. in my example $r(t) =$ the ...
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### PSD and $\lim_{T\rightarrow \infty} \frac 1 {2T} \int_{-T}^T x(t)\bar y(t)\,dt$

From Wikipedia, I taken a definition of power spectral density: For continued signals that describe, for example, stationary physical processes, it makes more sense to define a power spectral ...
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### How identify echo patterns in audio samples

How do I estimate if in recorded sound samples is present an echo caused from walls reflection ? (maybe there are multiples echoes: delayed, attenuated versions of the signal itself). I'm recording ...
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### How to find the fundamental frequency of a discrete signal using partial autocorrelation?

I hope you can help me with this question. I am trying to calculate the fundamental frequency (to know the beats per minute) of a cardiac pulse signal using partial autocorrelation. I use a 12-bit ...
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### xcorr in MATLAB for periodic function

I have a periodic signal and I want to find it's autocorrelation function. I can calculate it exactly: $$R_{uu}(h) = \frac 1M \sum_{k=0}^{M-1} u(k)\cdot u(k-h)$$ But will ...
942 views

### Getting a more accurate frequency read from autocorrelation and peak-detection algorithm

For a project I am attempting to create an automatic tuner for a guitar, which reads the audio from the guitar jack, determines the frequency and adjusts the string by a motor. Using http://www....
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### Least Squares and Auto and Cross Correlation

I am trying to understand why auto and cross correlation helps find the best fit line in least squares. I have an equation as stated here: $Ax=b$ -- I have not exact solution, so I use the least ...
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### Determining the uncertainty of an autocorrelation

My problem should probably be built up from the beginning, so lets start there. I performed a certain experiment 25 times. Every time, the experiment consists of 5000 measurements, and each ...
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### Measure of harmonicity in a time-series

I'm analyzing speech signal for identifying voiced and unvoiced regions. Voiced regions are supposed to have a "pitch", which can be estimated using auto-correlation function (ACF). Basically, one ...
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### How to calculate auto-correlation of a bpsk modulated signal or how to calculate expectation value of complex exponential function

How to calculate auto-correlation of a bpsk modulated signal, or how to calculate expectation value of complex exponential function manually not by using matlab or any other software? For example, if ...
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### Why autocorrelation can be more efficiently calculated using the fft

Can anyone explain why autocorrelation can be more efficiently calculated using the fft ?
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### Mathematical description of the ACF using fft2

I computed the acf of an image with the following code: ...
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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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### 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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### finding period with autocorrelation is not correct

I have recorded a signal, which I know is periodic (apart from noise). The period length is unknown. I want to extract the last period from the signal. Before going to a noisy signal, I first tested ...
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### Should I observe a signal multiple times for MUSIC algorithm?

In a paper Multiple emitter location and signal parameter estimation, the well-known MUSIC algorithm starts by calculating covariance (autocorrelation, whatever) matrix with: where overlines stand ...
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### Finding the deterministic autocorrelation function (ACF) from its power spectrum

The power spectrum of a stationary discrete-time random signal is $$\Phi_{xx}(e^{j\omega})=\begin{cases} 1 & |\omega|<\pi/2 \\ 0 & \pi/2 <|\omega| \le\pi \end{cases}$$ (a) ...
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### Auto correlation definition

My question has to do with the definition of auto correlation/cross-correlation for random processes. Oppenheim/Schafer (Discrete time Signal Processing, Pg. 815 (Appendix A.2),2nd ed.) define auto ...
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### Division by zero in Levinson–Durbin recursion?

I am doing a LPC analysis of a speech signal using the autocorrelation method. To calculate the LPCs I am using the Levinson–Durbin recursion. In my literature the error is initialized with the first ...