Questions tagged [autocorrelation]

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

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Train Pulse Recognition in Medium Voltage Networks

I just started a project in the Smart Grids area. It involves the recognition and quick extinction of earth faults in a medium voltage system. The system works automatically and pretty much gets rid ...
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196 views

Random signal modeling with Matlab

I want to build a detector of sorts. Say I have a bunch of signals and they all share some patterns, like some peaks in frequency or something more complicated that I can't bother to calculate by hand....
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659 views

What is the best pitch (frequency detector) for a Voice Activity Detection Algorithim?

I am programming a Voice Activity Detection algorithm. After researching several methods, I implemented a simple method that determines whether or not the person is speaking based off the RMS of the ...
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203 views

Evaluating auto correlation strength (Gamma)

I'm working on Cognitive Radio in TV Band Spectrum. I need to sense the presence of signal in a particular spectrum. I have to sample the incoming signal (say 1000 samples) and I have to find the ...
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304 views

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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1answer
1k views

Obtaining power spectrum from ACF, FFT using Matlab and FFTW

I am using Matlab R2012b 64-bit on Windows 7 in order to estimate the power spectrum of a simple signal that is: $$\cos(10t) + \sin(20t) $$defined in the time interval from 0.0 to 10.0 Here is what ...
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47 views

Relation between $X(f)$ and $S_x(f)$

We know that for a signal $x(t)$, it is related to $R_x(\tau)$ as, $$R_x(\tau) = \int_{-\infty}^{\infty}x(t)x(t-\tau)dt$$. $\\$We also know that $$R_x(\tau) \rightleftharpoons S_x(f)$$ $\\$How do we ...
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271 views

Power spectral density of $\left(x(t)\right)^2$?

The relation between $x(t)$ and output $y(t)$ of a non-linear device is expressed as $$y(t) = (x(t))^2$$ Let $x(t)$ be zero-mean stationary Gaussian random process with auto-correlation $$R_x(...
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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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3answers
83 views

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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48 views

How is the energy of $x_1\cdot x_2$ related to the energies of $x_1$ and $x_2$?

Let's say first signal x1 = [1 2 3 4], second signal x2 = [0.08 0.77 0.77 0.08] (Hamming window), third signal ...
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60 views

What is the meaning of **Sample** in **Sample ACF**

What is the meaning of Sample in Sample ACF (autocorrelation function)
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219 views

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_{...
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706 views

Autocorrelation of a signal comprised of only the same number

In MATLAB I generated a signal and its autocorrealtion function using: signal = ones(1,500).*5; % a vector of the number 5 acf = autocorr(signal,numel(signal)-1)); To my suprise the resulting ...
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83 views

Kronecker delta instead of dirac delta as correlation function of white noise

From my understanding, if you have a sample $x_{t_1},\dots,x_{t_n}$ of $X_{t_1},\dots,X_{t_n}$ which are iid $N(0,1)$, then $x_{t_1},\dots,x_{t_n}$ is a sample path of Gaussian white noise. However, ...
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52 views

Autocorrelation to diagnose faults

I'm attending a very practical course on signals and i have some doubts, i hope to receive answers in layman terms. 1) My prof said i can use the autocorrelation of the output of a process to ...
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352 views

While finding the ESD/PSD of a signal why we always prefer to find it via Auto-correlation function then the square of the FT of the signal? [closed]

In a video i saw that while calculating ESD or PSD of a signal time auto correlation function was used when it can be also done by the square of FT of the signal.Why we followed that approach even ...
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487 views

Autocorrelation strange results?

I'm trying to do autocorrelation with numpy in python but i'm getting strange results : For a simple 440Hz sine wave sample : This is the result of autocorrelation : Is this normal ? Maybe I'm not ...
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907 views

How to estimate the autocorrelation from nonuniformly spaced data

Assume a continues-time random process $X(t)$ sampled nonuniformely in time to acquire discrete signal $x[n]$. The sampling times are known but the autocorrelation is not. Is there an accurate ...
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1answer
118 views

Video: Detecting a digital timer and when it ticks

Input: A video with a digital timer, possibly several hours long, such as this video. The timer might use any font or color, and might be located anywhere on the video, but it probably won't fill the ...
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1answer
15k views

Autocorrelation function of a discrete signal

For a certain experiment of which I have data, I want to calculate the autocorrelation of the measurements. For this I used the expression from Wikipedia, which reads Here, $n$ is the dataset's size, ...
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2answers
1k views

Matching two audio inputs (signals) [duplicate]

this is for an application in which passwords are stored in the form of audio inputs . In order to provide user access , the password(in audio form) will be matched with already stored password(audio ...
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1answer
62 views

Calculate autocorrelation of a sinus

I am a beginer in signal processing. I am currently studying a signal $s(t) = \cos(h(t))$, and I have to calculate its autocorellation. Since $h(t)$ is periodic of period $T_s$, I calculated the value ...
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84 views

Does a signal and its autocorrelation ever have the same Fourier spectra?

My understanding is that Fourier power spectra give the frequencies and corresponding intensities/amplitudes contained within a signal. In certain techniques, such as molecular dynamics, it is common ...
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39 views

Auto-correlation of C/A code with 30dB noise

I've a C# program that generates a GPS C/A code consisting of -1s and +1s. Auto correlating the code with rotated versions of itself shows that the peak is 1023 and the next maximum value is 63 which ...
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996 views

Autoconvolution vs Autocorrelation

I have a serious doubt about Autocorrelation and AutoConvolution. My understanding is, Autocorrelation Autocorrelation is ...
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2answers
78 views

About using Walsh matrix as spreading sequence

I'm asking about some details about using the Walsh matrix as spreading sequence code. For example, suppose I'm using a $4\times 4$ Walsh matrix given by $$H = \begin{pmatrix} 1 & 1 & 1 & ...
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1answer
278 views

Confusion about ensembles and averages in autocorrelation matrices

I just noticed that until now I often don't cared about the scaling of the autocorrelation Matrix in Matlab. I then checked with the book Statistical Digital Signal Processing from M. H. Hayes. There ...
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246 views

Autocorrelation sequence in terms of Fourier transform of the underlying signal

Let $x(n)$ be a sequence of length $N$, which is zero outside the interval $(0,N-1)$. Let $X(k), k=0,1,\cdots,N-1$ be the FFT coefficients of $x(n)$, that is, $X(k)=\sum_{n=0}^{N-1}x(n) \exp\left( -\...
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115 views

Can spectral density be a complex quantity?

I have a signal ($S(t)$) which is product of a Gaussian ($G(t)$) and a random phase function ($e^{i\theta(t)}$, here $\theta(t)$ is a random function), as shown below $S(t)=G(t).e^{i\theta(t)}$ If I ...
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34 views

Practical insightful time domain functions [closed]

This question might be a little bit different, but i am having hard time to find some sort of a list/book/website/advice, with very practical time domain functions that provides useful insgihts for a ...
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67 views

What does a star shaped autocorrelogram mean?

Using the data in the upper graph, I get the weird autocorrelogram of the lower graph:- I've never seen a autocorrelogram of this shape. They're usually flat along the x axis. Testing the code with ...
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26 views

detection of periodicities in n-dimensional signals

Generally speaking, what analyses are necessary and sufficient for the detection of periodicities in an n-dimensional signal amounting to a discretely sampled density distribution over n-dimensional ...
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2answers
71 views

Synchronization with a specified sequence

I'm currently creating a project in Matlab where I'm simulating a communication, based on the SSB modulation, between a transmitter and a receiver. I've added a Barker sequence in the trasmitted ...
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2answers
532 views

Ornstein Uhlenbeck with drift

The Ornstein-Uhlenbeck (OU) process $dX_t = -\frac{1}{\mu} X_t + \sqrt{\frac{2\sigma^2}{\mu}} dW_t $ generates coloured noise with autocorrelation function $R(t) = \langle X_t,X_{t'}\rangle = \...
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109 views

Calculation of autocorrelation - does calculation “loop”?

With a delay $l$, autocorrelation is defined as: $$r_{xx}(l) = \sum_{n=-\infty}^{\infty}x(n)x(n-l) = \sum_{n=-\infty}^{\infty}x(n)x(n+l).$$ I want to calculate the autocorrelation of a signal $$x(n)...
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257 views

Finding number of independent samples using autocorrelation

I have a pressure signal (y) with 512000 samples and with a sampling frequency ...
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1answer
2k views

Pitch estimation using the autocorrelation method

I have the following code: ...
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1answer
292 views

What is the significance of a spike like autocorrelation function

I have some questions and doubts to which the answers are difficult to extract from text books. Hence I have posted this question here. Help would be extremely beneficial. Thank you. (1) The ...
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1answer
326 views

Auto-covariance of the product of deterministic and wide-sense stationary signal

Anybody give me an advice how to find the auto-covariance of the product of deterministic and wide-sense stationary signal. I couldn't find how to solve this, I have looked and searched the internet, ...
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3k views

How to find the period of a noisy signal using MATLAB's $\tt xcorr$?

Here is my code: function [ T ] = FindPeriodicity2(x,Fs) ac=xcorr(x,x); [~,locs]=findpeaks(ac); T=mean(diff(locs)/Fs); end and when I pass the signal ...
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612 views

Evaluation of Autocorrelation and Power Spectral Density of white noise through a filter

So say there's a filter with an impulse response of $h(t) = (0.8)^t u(t)$. I'd like to pass white noise through this and figure out the autocorrelation and power spectral density of the output. I'm ...
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1answer
2k views

Autocorrelation for the sum of a deterministic and stochastic signal

so I'm working on a problem where I need to find a PSD for the sum of a deterministic and stochastic function. So assume $x(t)$ being this sum: $x(t) = d(t)+s(t)$ where $d(t)$ is the deterministic ...
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110 views

Linear Prediction Coefficients

I want to learn how to compute linear coefficient, but to be honest - I can't. I know how to use them if i have it and why I want them. Suppose this toy example: A signal $x=[-1, -2, 0, 1]$ ...
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Determining Power Spectral Density from Autocorrelation Function and Time-Series Data

So I think I've confused myself a bit here. I know that taking the FFT of time-series data (wind velocities, for example) yields a power spectral density. However, I just read that taking the Fourier ...
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132 views

How to get the melody from a signal

I'm trying to retrieve a melody from a signal (simple sine with 3 notes). I've windowed the signal and performed autocorrelation to get the fundamental frequency of each window and then converted ...
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1answer
711 views

Autocorrelation of a stochastic process which is a sum

Let's say that a stochastic process is defined as $$X(t) = \sum_{n = -\infty}^{+\infty} X_n * f(t- nT)$$ where $X_n$ is the $n$-th symbol among independent random symbols. I have proved that $\...
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2answers
208 views

Simplification of a convolution-like expression

I am trying to further reduce the following expression (if there's a nicer way to write it): $\sum_{k=-\infty}^{+\infty}\sum_{p=-\infty}^{+\infty} \sum_{l=-\infty}^{+\infty} w(k) \varphi_\mathrm{y}(l-...
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1answer
17 views

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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2answers
111 views

Autocorrelation function and correlation integral

I am confused by the definition of autocorrelation function. It is originally defined as the expected value $$R_{XX}(\tau) = E[(X(t)X(t+\tau)] = \langle X(t)X(t+\tau)\rangle\tag{1}$$ where $\langle\...

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