Questions tagged [autocorrelation]

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

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5answers
11k views

Where does the delta function come from if we derive autocorrelation directly?

I am reading a book "Creating Noise" written by Hollos & Hollos and have a question about the autocorrelation function of the Gaussain white noise when reading the following passage: From the ...
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0answers
76 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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1answer
572 views

Finding the deterministic autocorrelation function (ACF) from its power spectrum

The power spectrum of a stationary discrete-time random signal is $$\Phi_{xx}(e^{j\omega})=\begin{cases} 1 & |\omega|<\pi/2 \\ 0 & \pi/2 <|\omega| \le\pi \end{cases} $$ (a) ...
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2answers
336 views

Auto Correlation for Time Frequency Analysis

Given a signal $x(t)$, how do I implement a form of autocorrelation function defined as $a(t,T) = x(t-T)x(t+T)$, where $T$ is an arbitrary constant? (a fast implementation would be ideal) Edit: ...
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1answer
1k views

AutoCorrelation Matrix vs Covariance Matrix for the MUSIC Algorithm [closed]

What is the difference between an autocovariance matrix and autocorrelation matrix?
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1answer
48 views

How is the energy of $x_1\cdot x_2$ related to the energies of $x_1$ and $x_2$?

Let's say first signal x1 = [1 2 3 4], second signal x2 = [0.08 0.77 0.77 0.08] (Hamming window), third signal ...
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1answer
1k views

How to prove that the peak of the autocorrelation function is at zero lag?

Show that for a signal $f(\tau)$ with finite energy and energy autocorrelation function $\phi^e_{ff} (\tau),$$$|\phi_{ff}^e (\tau)| \leq \phi_{ff}^e (0), \ \ \forall \tau.$$ According to my textbook ...
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1answer
770 views

Golay complementary sequences in 802.11ad

The Golay complementary sequences consist of two sequences of the same length $N$ such that there acyclic autocorrelation sequences have sidelobes equal in magnitude but opposite in sign. So, when the ...
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1answer
341 views

Decorrelating Stationary Colored Gaussian Noise — Effect On The Desired Signal

So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$. In ...
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1answer
2k views

Determining the fundamental frequency/pitch of a note

What I am trying to achieve is getting the fundamental frequency of a note played by an instrument. What I have already done is performing an FFT on a samples of audio file, and here's what I get: ...
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1answer
151 views

How is the matrix $\mathbf R_x$ not Toeplitz in case of a signal missing one term?

I am solving a question that says if we have sequence $x(n)$ of a signal missing one term then we have to find autocorrelation matrix $R_x$ as follows: $$R_x = E\{\mathbf {xx^H}\}$$ Now if I take $...
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0answers
365 views

Finding phase of fundamental from autocorrelation

I have some code, shown below that I have been using to find the fundamental of a guitar string. After this function is called, I go thru the real buffer and find the peak, whose location gives me ...
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1answer
777 views

Determining the autocorrelation sequence from an AR model

I have the following equation: $$x(n)=\frac{14}{24}x(n-1)+\frac{9}{24}x(n-2)-\frac{1}{24}x(n-3)+w(n)$$ where, $w(n)$ is a stationary white noise process with variance $\sigma^2_w$ Now, I want to ...
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1answer
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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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1answer
282 views

Evaluating the spectral density of generated noise through the autocovariance

I'm working on generating noise signals $X(t)$ (with $t \in \left[0,T\right]$ with step size $\delta t$) with a prescribed power spectral density $S_{XX}(f)$ and I'm figuring out how well I am ...
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4answers
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Finding the Amplitude of a Sinusoid in Noise

I'm trying to solve for the amplitude and frequency of a sinusoid embedded in zero-mean gaussian white noise. I am supplied a sample file of a 40000 element array. I first took the autocorrelation ...
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0answers
24 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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1answer
608 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
183 views

Autocorrelation question

I am trying to get an understanding of autocorrelation and I am having some issues with trying to understand the process. I have a Bernoulli process called $X[t]$. In this process, $P(X[t] = 1) = p$ ...
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1answer
244 views

Autocorrelation of a noisy linear map

I am interested in calculating the autocorrelation function of a linear map with some noise (model given below) but am slightly confused in doing so. At first, I did not realize there were two ...
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1answer
193 views

Auto correlation definition

My question has to do with the definition of auto correlation/cross-correlation for random processes. Oppenheim/Schafer (Discrete time Signal Processing, Pg. 815 (Appendix A.2),2nd ed.) define auto ...
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4answers
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Recommendation for book - Writing DSP code in C

I am looking for some good book, that simply show how you actually write a code in C, to do all the main DSP methods . FFT. Low-pass and high-pass filters. Auto-correlation. Noise processing. And ...
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1answer
255 views

How to implement Cross Spectral Density [duplicate]

I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image. Reading wiki1,wiki2,wiki3 from wikipedia, and ...
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1answer
286 views

The way to measure chromatic tuners' precision

I have a question about measuring precision of chromatic tuners. I want to divide 2 cases. CASE1: link; Korg AW-2G's precision If you check the link or this picture, it says that Korg AW-2G has ...
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2answers
982 views

Getting a more accurate frequency read from autocorrelation and peak-detection algorithm

For a project I am attempting to create an automatic tuner for a guitar, which reads the audio from the guitar jack, determines the frequency and adjusts the string by a motor. Using http://www....
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2answers
1k views

finding the fundamental frequency in frequency domain

I want to get the fundamental frequency of a signal. I used a time domain approach first. It just sums up the differences between the signal (lets say 2048 samples) and the delayed version of the same ...
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1answer
642 views

How do I calculate the autocorrelation of a train pulse having only the pdf?

I have a pulse train of a fixed period, but a random amplitude following a Gaussian distribution $(\mu=0,\sigma=1)$. I know how to work with a random period or delay, but how do I proceed to calculate ...
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0answers
840 views

Multiplication of two noise

I have a question on the multiplication of two noise. Suppose I have two noise $n_1[n]$ and $n_2[n]$. I only know their power spectral density $N_1[k]$ and $N_2[k]$. How can I get $N_3[k]$, where $...
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1answer
420 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 ...
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1answer
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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. ...
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3answers
266 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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1answer
416 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 ...
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1answer
705 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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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. ...
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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 ...
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0answers
325 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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2answers
156 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 density ...
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1answer
237 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 ...
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1answer
176 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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1answer
2k 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
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.
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4answers
2k 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 ...
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1answer
732 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 ...
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0answers
54 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. ...
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1answer
107 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
770 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{...
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1answer
896 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 ...
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0answers
380 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 ...
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1answer
47 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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0answers
96 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 ...

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