Questions tagged [autocorrelation]

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

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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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281 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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464 views

Autocorrelation of Addition of Two Independent Signals

Given a random signal $ Z \left( t \right) $ which is addition of two independent signals $ X \left( t \right) $ and $ Y \left( t \right) $ with constant parameters $ a $ and $ b $: $$ Z (t) = aX(t) +...
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439 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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1answer
793 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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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
14k 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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33 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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1answer
462 views

Autoconvolution vs Autocorrelation

I have a serious doubt about Autocorrelation and AutoConvolution. My understanding is, Autocorrelation Autocorrelation is ...
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2answers
74 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
152 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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160 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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62 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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1answer
61 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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23 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
63 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
430 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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2answers
84 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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2answers
147 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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2k views

Pitch estimation using the autocorrelation method

I have the following code: ...
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1answer
261 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
306 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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1answer
2k views

How to extract prosodic cues from a wav file using Python

How do I extract the following features as from wav files in Python - Voicing rate (Voice rate) - frequency of phonemes while speaking, and represents the pace of a conversation Number of ...
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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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568 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
1k 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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1answer
97 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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1answer
3k views

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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1answer
631 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
163 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
25 views

Autocorrelation Computation with MATLAB

I have done the computation of the autocorrelation of a sequence (vector), here called "frame", and I have plotted it. Here the code: The resulting graph is: I do not understand the position of the ...
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1answer
48 views

Are there any signals with brickwall autocorrelation?

Are there any signals whose autocorrelation $R(\tau)$ has the following form? Assuming $\tau_c > 0$ and $R_0 > 0$ a constant, $$R(\tau) = \begin{cases}R_0, \text{ for $|\tau| < \tau_c$} \\ 0,...
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2answers
84 views

Correlation between 2 signals of uneven dimensions

As a part of my work, I am trying to correlate the audio signal in a video with the pixels of each frame. The steps I follow are: Audio sampling rate and frame rate of the video are known. So, ...
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1answer
1k views

Autocorrelation: numpy versus FFT

I have a series a of values (0 and 1) coming from a Brownian process with drift for which I am studying the autocorrelation. I used two methods: 1) numpy autocorrelation: ...
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1answer
15 views

How can faux correlated data be generated for testing or training?

There are one or two questions here that ask how to assess data correlation. The data tends to be empirical. Is there some tool or standardised technique for generating correlated data from scratch? ...
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1answer
260 views

How to determine fundamental frequencies (beats/minute) of heartbeat? (matlab)

read = matfile('ECG.mat'); [cor, lags] = xcorr(read.ecg, read.ecg); read.Fs; So i have read.ecg (signal) and ...
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1answer
231 views

Problem understanding the Expectation Operator

I know that the Expectation Operator $E\{x\}$ four discrete values is $$ \sum_k \alpha Pr(x = \alpha_k)$$ and its very intuitive when speaking out a formula which contains the Expectation Operator. ...
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1answer
131 views

Correlation of a signal

I have one sample for a signal. This sample is a vector of length 384. I need to calculate the correlation matrix for this signal,So I need many samples for the same signal. How can i generate these ...
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1answer
37 views

Question on Levinson's proposed discrete form of Wiener filter

The whole foundation of Levinson's discrete version of Wiener filter is based on the assumption of stationarity of a time series, and aims to predict a value based on the past observed values. Now, if ...
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1answer
255 views

Wiener Filter in Frequency Domain: What it does to a specific Frequency?

As I understand Wiener filter in time domain tries to estimate a signal as close as possible to its (original) non-degraded signal using the degraded signal by white noise. $$H(\omega)=\frac{\Phi_{...
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1answer
400 views

Matrix cross correlation in python

I'm currently performing matrix cross correlation in python using : C = scipy.signal.correlate2d(A,A) where A is a 2D matrix, typically a picture. As you can ...
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1answer
1k views

Show That the Power Spectrum Density Matrix Is Positive Semi Definite (PSD) Matrix

Given a Wide Sense Stationary Multi Variate (Vector) Random Process $ \boldsymbol{x} \left[ n \right] $ it Auto Covariance Matrix Function is given by: $$ {R}_{x, x} \left[ m \right] = \mathbb{E} \...
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1answer
168 views

Estimating confidence intervals for the mean value

Say I conducted a numerical experiment -a time-dependent fluid simulation- and extracted a time-series of some variable. It looks like this: As a result of the simulation, I am supposed to report the ...
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1answer
539 views

What kind of filter I should use to remove the oscillations in this autocorrelation function?

I have an autocorrelation function which is shown as following, I do believe these trailing oscillating wigs are spurious and should be removed by some kind of filter. But I am not familiar with any ...
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1answer
996 views

How to calculate autocorrelation function of an image noise

I am trying to calculate the autocorrelation function of an image noise. Specifically, I want to calculate the NCORR parameter in the function deconvwnr(). I have knowledge about the noise, which is ...
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1answer
697 views

What's wrong with this Average Magnitude Difference algorithm?

I implemented this Average Magnitude Difference algorithm in Javascript ...
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1answer
793 views

Time-domain cross-correlation with padded signals [closed]

I have a frequency domain cross-correlation implementation written in C (based on: https://github.com/dMaggot/libxcorr). It uses the library FFTW3 and this is the gist of it: ...
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1answer
72 views

Dependence of $\tt n$ in $\tt fft(data,n)$ in auto correlation of data

The followings are results of autocorrelation of an 'image'(1*) (subplot 221) using xcorr, n point ...