Questions tagged [autocorrelation]

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

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446 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
346 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
338 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
785 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 $f_0$, $A$ ...
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)...
2
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0answers
46 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
202 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}(\...
2
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0answers
216 views

Pitch detection, YIN, pYIN

So here is the "seminal" YIN paper: Cheveigne A, Kawahara H. - YIN, a fundamental frequency estimator for speech and music and the new, improved probabilistic YIN: Mauch M, Dixon S. - PYIN: A ...
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0answers
82 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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2answers
282 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
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). ...
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0answers
2k 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 ...
2
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0answers
135 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-...
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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
297 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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0answers
56 views

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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0answers
11 views

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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0answers
90 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
57 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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30 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
72 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
54 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
385 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
85 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
104 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 ...
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0answers
339 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
74 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
304 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
73 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
23 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
190 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
144 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
357 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
266 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
275 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
194 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
649 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

Stereo echo cancellation for stationary source locations: why does adaption stagnate?

In a stereo echo cancellation system, the echo path for the far-end-signal in the near-end room is estimated by an adaptive filter. Since the same signal is transmitted by two similar far-end paths, ...
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0answers
17 views

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 ...
0
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1answer
35 views

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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0answers
19 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
35 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
28 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 $X_t = c\ \text{cos}(\omega t)$...