# Questions tagged [autocorrelation]

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

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### 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 ...
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### 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. ...
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 ...
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### 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 ...
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 ...
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### 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. ...
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### 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 ...
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 ...
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### 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 ...
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 ...
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 ...
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### 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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### What is the unit of autocorrelation function?

In general, for autocorrelation of the deterministic signals,from the formula what is the unit of it.
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### 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 ...
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### 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 ...
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### 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. ...
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### 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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### 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{...
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### 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 ...
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 ...
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 ...
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### 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 ...
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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 ...
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-...
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 ...
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 ...
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### 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 ...
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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### 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 ...
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### 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 ...
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 ...
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### 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: ...
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 "...
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### 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-...
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### 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 ...
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### 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 ...
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### 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 ...
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,...