Questions tagged [autocorrelation]

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

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Power spectral density of sinusoidal signal in noise

In a literature I face with this input and power spectral density (PSD) $$x(t)=s(t)+n(t)=A\cos\left(\omega_c t +\phi\right) + n(t)$$ first I want to know How can we find PSD of $\cos\left(\omega_c t ...
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Calculating the fundamental frequency using Autocorrelation often gives half the expected value

I'm currently writing a mobile app which needs to analyse musical notes and find the fundamental frequency to determine the pitch. To do this I'm reading in audio data, taking an FFT, taking the auto-...
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1answer
674 views

Does the Wiener–Khinchin-Einstein theorem hold for non-Gaussian processes? If so are there any assumptions?

The Wiener–Khinchin-Einstein theorem states that the auto-correlation $(r_{xx}(\tau))$ and spectral density $(S(f))$ are Fourier duals, i.e. $$r_{xx}(\tau) = \int^{+\infty}_{-\infty} S(f) \exp\left( ...
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Autocorrelation matrix derivation

Hi I am trying to derive the autocorrelation matrix and I am unsure about how exactly it works. I can see that the $4\times 1$ matrices result in the Hermitiain and Toeplitz matrix? Surely the only ...
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1answer
418 views

Normalized autocorrelation of a sum of two signals

I obtained the autocorrelation function of a sum of two signals: as but I want to know what is the normalized autocorrelation of above equation?
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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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3answers
293 views

Could there be any reason to prefer convolution-based calculation of autocorrelation?

Theoretically both of ways of calculating autocorrelation function are identical: strightforward convolution and Fourier-based method where we use FFT/iFFT in practice. And as it is well known, the ...
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1answer
349 views

What does the frequency axis of a Power Spectral Density mean?

I have never really understood what the frequency axis meant when we plot the Power Spectral Density(PSD). Does it correspond to frequency as we get after we take the Fourier Transform of a time ...
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1answer
575 views

Finding the fundamental frequency from Autocorrelated data

I'm writing an app in which I need to find the fundamental frequency of a note produced by a trombone. To do this I'm taking the FFT of audio data from a microphone and then using autocorrelation code ...
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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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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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454 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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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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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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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
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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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635 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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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
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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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135 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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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
657 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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613 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 $f_0$, $A$ ...
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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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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
521 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
150 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
193 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
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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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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
197 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
264 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
893 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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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
479 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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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
345 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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774 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. ...
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3answers
249 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
390 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
574 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
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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 ...
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297 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
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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 ...
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1answer
206 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
159 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
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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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1answer
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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.