Questions tagged [autocorrelation]

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

Filter by
Sorted by
Tagged with
0
votes
1answer
370 views

Correlation in DSBSC modulation

Suppose we have a DSBSC signal given by : $$s(t) = 10 \cos (2\pi f t + \phi ) \cdot m(t) $$ where carrier is random signal with phase ($\phi$) uniformly distributed in $[0,2\pi]$. If ...
-2
votes
1answer
866 views

Correlation using fft and xcorr and plot both answers (Matlab) [closed]

I am trying to calculate autocorrelation using fft and xcorr and plot the grafhic with both cases. ...
1
vote
3answers
261 views

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 ...
0
votes
1answer
402 views

How do I interpret these autocorrelograms?

Hello signal processing wizards. I am young and feeble, and would like some help interpreting my spike-train autocorrelograms of six isolated neurons. These histograms were created using the code ...
5
votes
1answer
628 views

Echo cancelling using autocorrelation function

I was given a problem, but I couldn't solve. I did some researches but I still didn't figure it out. Here is the problem: An audio signal $ s(t) $ is generated by a speaker reflects in a wall with ...
1
vote
2answers
3k views

Matlab - How to create an autocorrelogram using a spike-train

I have already posted this question on MATLAB's question forum. However, I haven't received any responses, and am hoping to find some folks who may be a bit more signal processing savvy on here. ...
9
votes
1answer
6k views

Auto Correlation vs Cross Correlation vs Convolution and their applications

I know from wikipedia that auto correlation in done on the same signal while cross correlation is done on different signals.But what does this actually imply in terms of application.I can always apply ...
0
votes
0answers
309 views

hamming window for LPC

I am working on a library for generating LPC for speech synthesis. I am currently using a hamming window for the spectral analysis which goes in 200ms blocks over the signal, and does the a-to-k ...
1
vote
2answers
141 views

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 ...
1
vote
1answer
210 views

Extracting direction of dominant sinusoids from an image in terms of angles

Here is a sample image. What I am looking to do is compute the dominant "wrinkle" directions. The dominant wrinkle directions can be seen in the following FFT, roughly, by drawing a line through the ...
1
vote
1answer
161 views

Power Spectrum Analysis

In order to find a peak or max response in the fourier domain as in the spatial domain, I have been studying bartlett's method, welch's method, and the blackman-tukey method for more accurate power ...
0
votes
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 ...
1
vote
1answer
2k views

What is the unit of autocorrelation function?

In general, for autocorrelation of the deterministic signals,from the formula what is the unit of it.
3
votes
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 ...
1
vote
1answer
666 views

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 ...
0
votes
0answers
51 views

Detecting two changing inharmonic pitches

I have a recording of a newer type of siren that uses two pitches sliding back and forth in time. I want to be able to detect both of the pitches simultaneously or overlapping at short intervals. ...
0
votes
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 $x=[-1, -2, 0, 1]$ ...
3
votes
1answer
653 views

How to get the autocorrelation of this finite discrete function?

This is the function: $$ x(n) = \begin{cases} 1, & \text{-N $\leq$ n $\leq$ N ;}\\ 0, & \text{otherwise.} \end{cases} $$ And I tried to solve it, using sigma notation or summation: \begin{...
0
votes
1answer
844 views

PSS convertion from Frequency to time domain

Hi I have a question regarding primary sync signal in LTE. It is generated in frequency domain and its length is 63. How to convert this signals frim frequency to time domain. Should I use IFFT? what ...
0
votes
0answers
349 views

Autocorrelation Lag In Seconds Explanation?

I am using a MatLab audio feature extraction toolbox (MIRToolbox), and I am in the process of cross correlating an onset curve (envelope). I am aware of what the lag means when using Matlab's ...
0
votes
1answer
45 views

Concepts Surrounding First Two Samples in Difference Equation

I'm attempting to construct a difference equation in matlab for the function u(n) and find the auto-correlation matrix R. I'm following the technique as is defined by my text below: The system I'm ...
0
votes
0answers
90 views

Length and spacing autocorrelation with FFT

I have calculated, with FFT and A-FFT, the autocorrelation of a discrete signal (coming from an integration) with spacing $\Delta T$ composed by $N$ samples padded to $2N$ with zeroes. What is the ...
0
votes
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 ...
0
votes
0answers
168 views

what kind of information we can get if the auto-correlation for an image is a ring or two rings?

I did the auto-correlation for an image by Mathematica. The auto-correlation function shows rings as follow..I am sorry that I can not attach the original image here. From the following auto-...
9
votes
1answer
3k views

What is an AMDF?

The wikipedia page for Average Magnitude Difference Function/Formula (AMDF) appears to be empty. What is an AMDF? What are AMDF's properties? What are AMDF's strengths and weaknesses, as compared ...
0
votes
1answer
567 views

why is the plot of the PSD of this autocorrelation function oscillating?

I was doing an exercise trying to compute the PSD of the following discrete autocorrelation function: \begin{equation} r_x(m) =(1/2)^{|m|} \end{equation} In this simple matlab code that I came up ...
6
votes
2answers
443 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 ...
0
votes
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 ...
0
votes
0answers
121 views

regarding autocorrelation and derivation of original signal

$$r_x(t)=\begin{cases} 2-2t ,& 0 \le t \le 1\\ 2+2t ,& -1 \le t \le 0 \end{cases}$$ So how do I get original $x(t)$ from this? I tried integrating the equations, and the value I got was ...
1
vote
3answers
688 views

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 ...
1
vote
1answer
259 views

Ambiguity function of multiple sines

I was reading through the Ambiguity function, and I was wondering if it's possible to calculate analytically (or numerically) the ambiguity function of a sum of sine waves. In case of a single sine ...
0
votes
1answer
423 views

autocorrelation A to K conversion for LPC speech analysis?

I am building an LPC analysis tool for speech synthesis and did the following to generate my a0 through a10: ...
0
votes
1answer
219 views

Auto/cross correlation of a cosine in the context of an adaptive beamformer

I am currently reading chapter 13 of 'Adaptive Signal Processing' by Widrow and Stearns, so if anyone happens to have a copy of the book to hand it could be helpful. I am reading the chapter on "...
1
vote
1answer
1k views

Improving an auto-correlation based guitar pitch detector

I've seen many questions on this forum regarding pitch detection for musical instruments (commonly guitar), and spent a while reading through the answers to create a basic implementation of auto-...
1
vote
1answer
352 views

Uses of peaks in audio auto-correlation

Do you know of any algorithms for audio processing that make use of peaks in auto-correlation function? I am currently involved in research on mapping methodology for dynamic algorithms. I came ...
0
votes
1answer
101 views

How do we compute distrubtions of the value of a random process conditional on initial conditions?

Suppose I have a stationary process $\phi(t)$ with a known autocorrelation function $$ A(\tau) \equiv \langle \phi(0) \phi(\tau) \rangle$$ and suppose I also know that $\phi(t)$ is Gaussian ...
1
vote
0answers
187 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. $ ...
0
votes
2answers
783 views

A filter in IOS to eliminate a certain frequency range

I am making an application where I record sound on an IOS device using the built-in microphone. I want to process the sound in such a way that only frequencies in the 16-18 kHz range remain; the other ...
-1
votes
1answer
203 views

Get a power spectral density from real random data

I am using real data of wind, which is a random one to get the power spectral density of these values. How can I do to get this PSD in matlab, and Can I get an analytical expression for this psd. ...
0
votes
0answers
980 views

Autocorrelation and FFT : avoid zero-padding

Some posts evocate the computation of convolution or cross-correlation using FFT and zero-padding the temporal signal. I want to compute the autocorrelation of a 3D array using FFTW (2 dimensions are ...
3
votes
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)...
1
vote
1answer
622 views

Kalman Filter Estimate vs ACF Least Squares Estimate

I am currently reading Chapter 5, Applications to the Gas Markets, in Stochastic Modelling of Electricity and Related Markets by Benth, Benth and Koekebakker, World Scientific, 2008. In the ...
0
votes
0answers
331 views

Equivalence of FFT and PSD based output based on the Frequency Response Function

Correct me please if I am wrong... I have just started working in the domain of signal processing using the Fourier Transform ($\mathbf{FFT}$) and Power Spectral Density ($\mathbf{PSD}$). I am trying ...
0
votes
1answer
551 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 ...
0
votes
1answer
1k views

Cross-Correlation : Comparing two signals or finding the location of a target

I read across places that cross-correlation of two signal (a radar sending a signal and receiving it back) one can detect the location (distance) of a target from a point and that cross-correlation ...
-1
votes
1answer
1k views

Correlation : Cross correlation why we need to multiply the samples

I understand what books states about cross-correlation of signals and their mathematical representation: For continuous functions f and g, the cross-correlation is defined as: $(f \star g)(\tau)\ \...
1
vote
2answers
4k views

Autocorrelation of white noise

Autocorrelation of white noise should have a strong peak at "0" and absolutely zero for all other $\tau$ according to this. Then why is output of this code a cone shape (with the expected of strong ...
2
votes
1answer
301 views

Correlation meter

I have three questions regarding the correlation meters used in audio. How are they calculated? I have heard correlation is performed by convolving one signal with the time flipped version of a other,...
1
vote
0answers
143 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 & \...
0
votes
0answers
440 views

Reliable peak picking algorithm?

I've written an application that estimates pitch based on autocorrelation function. I did peak picking by comparing vector values to determine whether the central one is a peak or not, but this method ...