Questions tagged [autocorrelation]

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

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437 views

Efficient calculation of correlation function every $N^{\rm th}$ point

I would like to calculate a long correlation function of length say, 1e6 points. I have a prior knowledge that the correlation peak will be in point k*1000. Is there an efficient way to apply this ...
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0answers
326 views

What is the autocorrelation equivalent of the spectrogram called?

I'm very knowledgeable about the differences between the Fourier transform, and the autocorrelation; mainly that one converts the time domain to the frequency domain, and the other finds periodicities ...
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4answers
1k views

Advice on autocorrelation via FFT

I have been creating an application in Java that transforms an audio signal and writes it to a midi file. At first I tried using autocorrelation to find the fundamental frequency. However, I have ...
3
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2answers
3k views

Correlation Using FFT / IFFT (Convolution in Frequency Domain) in Java

I try to find about the delay between two audio files using Cross Correlation in Java. I've already done this algorithm so far that i get a idea about how many samples is the delay. FFT x1 -> Zero ...
3
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0answers
336 views

Remove the extra peaks by lag

Suppose that we have some peaks of a signal and we know the time lag between dominant peaks. How is it possible to remove the extra peaks by applying time lag ? Lets say it in MATLAB ...
3
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1answer
2k views

How to construct Polyphase (Frank) codes in MATLAB

I have written a piece of code in MATLAB to generate Frank codes - Pastebin link for pulse compression. I know that Frank codes are stepped frequency approximations to Linear Frequency modulation(LFM)...
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0answers
38 views

what is equal to the FT of the Autocorrelation function

I am trying to make my own demonstration in order to find what is equal to the FT of the Autocorrelation function. The autocorrelation function in some book about turbulence is defined as: r($\tau$)=...
2
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2answers
149 views

Autocorrelation of signal with offset

If I have a stationary signal $x(t)$ with zero mean and with an auto correlation $r_{xx}(\tau)$, then what is the auto correlation of $y(t)=x(t)+b$ ? My calculations so far: $$\begin{align} r_{yy}(\...
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0answers
70 views

How to visualize the autocorrelation matrix and it's properties

Having a hard time wrapping my head around autocorrelation matrix as it applies to a spectral estimation problem like MUSIC or ESPRIT. If the signal vector contains a summation of sinusoids in noise, ...
2
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0answers
161 views

Autocorrelation of a signal with gaps

I am trying to find the analytic expression of the autocorrelation function for a signal $X(t)$ which is defined as follows. $X(t = 0) = 1$ At random times jumps to $X(t) = 0$ happen The jump ...
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0answers
3k views

Spectral Correlation Function estimation using FAM method — implementation help

I am trying to estimate the Spectral Correlation Function by the FFT Accumulation Method (FAM) in Matlab. The way I understand the FAM method is as this link (see page 6 & 7 for FAM tutorial). ...
2
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0answers
1k views

How are the time scales of an exponential decaying autocorrelation related to the duration of peaks?

I'm reading a biology article (full text here) that analyzed the variation of a cell parameter over time at different stimulus intensities (calcium concentration). The frequency of peaks increases at ...
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0answers
129 views

Iterative Auto and Cross Correleation Estimates

I'm looking for literature or other information that covers iteratively estimating the auto- and cross-correlation vectors and the auto-correlation matrix. Initially, I can assume the signal is wide-...
2
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0answers
70 views

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 ...
2
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0answers
285 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 ...
2
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1answer
645 views

Calculation of an autocorrelation function

A sample of a random process is given as: $$ x(t) = A\cos(2\pi f_0t) + Bw(t) $$ where $w(t)$ is a white noise process with $0$ mean and a power spectral density of $\frac{N_0}{2}$, and $f_0$, $A$ ...
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0answers
49 views

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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0answers
48 views

Equivalence of the Power Spectral Density definitions

I am trying to show the equivalence of the following Power Spectral Density definitions in Matlab: Definition 1: $$ P(\omega) = \sum_{k=-\infty}^{\infty} r(k)e^{-j\omega k} $$ Definition 2: $$ P(\...
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29 views

How to add noise with given autocorrelation to signal in Matlab?

My question is a mix of signal processing and Matlab coding. I have an FIR filter with added noise $w_n$ $$x_n=\sum_{m=0}^{N_h-1}h_mg_{n-m}+w_n.$$ Now the noise $w_n$ has the autocorrelation $$E[...
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0answers
55 views

Zero-padding vs. nonzero-padding in computation of auto-correlation with FFT

Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal? If I have a measured signal which has good ...
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0answers
49 views

How to deduce the shape of autocorrelation graphically?

I'm asking for your help in understanding if I have a rectangular function, so the autocorrelation for it will be triangular... and I can prove that graphically but this is time-consuming especially ...
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0answers
36 views

$E(X(t)X(t))=\sigma^2\delta(\tau)$ or $E(X(t)X(t))=\sigma^2$

(Question already asked on Math StackExchange) Let's say we have a white noise process $x(t)$ such that: $E(X(t)X(t+\tau))=N\delta(\tau)$ $E(X(t))=0$ In particular, with $\tau=0$, $E(X(t)X(t))=E(X^...
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1answer
317 views

Confusion about PSD and RMS

Let's say I have a noise power-spectral-density (PSD) which is not flat and ranges from 0 to $f_1$ Hz in frequency. As we know, the total area under the PSD is equal to the total average power of the ...
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2answers
80 views

Image Interpolation Using the Yule Walker Equations

I have been studying about the Yule-Walker equations for prediction of a time series data from knowledge of past values of the series. Is there any way I can use the same in an image to exploit the ...
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0answers
98 views

Subtracting audio signal emitted - trying to use spectral subtraction to localize moving objects

I am a Software Engineer without much signal processing background and currently spending and experimenting to get use to it. My scenario: Assume a speaker and a microphone array. A speaker emits an ...
1
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2answers
262 views

Harmonics to Noise Ratio Estimation

I'm willing to estimate the Harmonics to Noise Ratio (HNR) of a speech signal x[k] and using autocorrelation method. Theoretically, HNR is given as, $\ HNR = \frac{R_{xx}[T_0] }{R_{xx}[0]-R_{xx}[...
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0answers
311 views

Power Spectral Density of a WSS Random Process with 2D Discrete Fourier Transform

I'm trying to understand how the random process (RP) signal in discrete time domain is related to its power spectral density (PSD) in frequency domain if the signal is wide sense stationary (WSS). If ...
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0answers
66 views

derive AR model based on the autocorrelation of jakes model

I am trying to derive the channel model based on the autocorrelation of Jakes model. In step 2, i am trying to get rid of $s(n+1)$ by inserting it to $s(n-k)$ in which the limit will change. However i ...
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0answers
290 views

Event detection in a running person's acceleration data

I am trying to detect some events on this signal : This is the acceleration of someone running. By eyes we can detect many blocs, sometimes separated by a little interval. I would like to be able to ...
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0answers
71 views

Autocorrelation of a $L$-point moving average system

The $L$-point moving system is: $$y[n]=\frac 1L\sum_{k=0}^{L-1}x[n-k]$$ $x[n]$ is a Bernoulli random signal with $\beta=0.5$ (equal probability) The autocorrelation of $x[n]$: $\psi_{xx}[m]=\delta[...
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0answers
22 views

Power Spectral Density Via Rank 1 Update

I know that I can find the autocorrelation matrix of a series of finite length sequences via rank-1 updates using the relation: $\mathbf{R}[k] = \frac{1}{k}\mathbf{R}[k-1] + \frac{1}{k+1}\mathbf{r}[k]...
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0answers
185 views

Construct a correlation matrix using the covariance method

I want to compute the autocorrelation matrix by using the covarience method. X(n) is the harmonic process $X(n) = \sum\limits_{i=1}^3 A_i e^{jn\omega_i} + V(n)$ $V(n)$ is unit variance noise. $ ...
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0answers
132 views

The autocorrelation of a WSS process as a linear operator

If I'm given a autocorrelation matrix of a WSS process what interpretation should I put on the resulting vector. More concretely the matrix takes the form $\begin{bmatrix} x_1 & x_2 & \...
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0answers
310 views

Noisy Signal auto/cross-correlation

I am trying to understand the basics of the cross/auto-correlation if the noisy signal $y(t)$ which is received from the channel at the receiver. Here at receiver we want to estimate the noise in the ...
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0answers
259 views

ACF and PACF Confidence Levels for ARMA

I'm trying to figure out where exactly to draw the confidence levels for the autocorrleation function (ACF) and the partial autocorrelation function (PACF) for an ARMA model. For PACF I found that a ...
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0answers
58 views

peak-to-peak test between two signal

Suppose that we have different signals (Pulses). I would like to study which signal has deterministic peak-to-peak distant (lag). For example A=[1 0 0 1 0 0 0 1 0 0 1] and B=[1 0 0 1 0 0 1 0 0 1] and ...
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0answers
266 views

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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0answers
192 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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0answers
640 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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0answers
202 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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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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0answers
17 views

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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0answers
25 views

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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0answers
27 views

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 $X_t = c\ \text{cos}(\omega t)$...
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0answers
26 views

Autocorrelation of an AR model

When I plot the autocorrelation function of an autoregressive signal, I get this instead of a damping sinusoid. I am having trouble understanding why this is happening. My signal is an generated ...
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0answers
35 views

SNR and Correlation

Signal to Noise ratio is essentially the ratio of the signal power to the average noise power. Correlation is the similarity of two signals. Assuming a signal travels through a channel or medium, and ...
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2answers
58 views

Why is there only one integration in the solution if there is two integral in the formula?

In this problem the random variable is theta and according to the formula there should be two integrations but in the solution there is only one . Nor am i able to understand the meaning of x1 and x2 ...
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0answers
43 views

ACF expression using FFT method

It is known that the ACF of a 2D digital image can be obtained by computing the inverse Fourier transform ...
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0answers
26 views

Is the expectation of a random process $X(t)$ with zero DC component necessarily zero?

Is the expectation of a random process $X(t)$ with zero DC component necessarily zero? Or can it be non-zero depending upon the process?
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0answers
19 views

Increasing error safety in the cross correlation of two binary signals in wireless communication

I want to cross correlate two binary signals, where one is corrupted by noise and shifted by a time constant $\tau$, but has the same bit pattern (so basically an auto correlation). Similar to case 2 ...