Questions tagged [autocorrelation]
Autocorrelation is the cross-correlation of a signal with itself.
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1answer
768 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:
...
2
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3answers
109 views
Weighted Sum of Auto Correlation - Lower Bound
Given a vector $ v $ with elements $ {\left\{ {v}_{n} \right\}}_{n = - \infty}^{\infty} $ and denoting $ {v}_{n}^{\left( k \right)} = {v}_{n - k} $, namely, a shifted vector by $ k $ elements (Mind ...
3
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1answer
640 views
Finding System transfer function, $H(z)$ or, equivalently, its impulse response, $h[n]$
I just started on DSP and I have a question that I would like to ask.
I have a zero-mean uncorrelated wide sense stationary discrete-time random process {$x[n]$, $n$ is a set of integers}. $x[n]$ is ...
2
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1answer
297 views
Fourier Transform gives unexpected results: signal reversal and conjugation
As far as I understand the math you can reverse a real valued signal by Fourier transformation, taking the complex conjugate of the result and inverse Fourier transformation, i.e.
\begin{equation}
\...
2
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3answers
201 views
How can define an indicator which measures the degree of similarity between two signals?
The similarity of two signals is calculated by cross correlation. But, how to define an indicator which quantitatively measures the degree of similarity between two signals? Thanks.
0
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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 ...
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1answer
254 views
Should I observe a signal multiple times for MUSIC algorithm?
In a paper Multiple emitter location and signal parameter estimation, the well-known MUSIC algorithm starts by calculating covariance (autocorrelation, whatever) matrix with:
where overlines stand ...
2
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1answer
2k views
Random process $X(t)$ with autocorrelation function given find the mean and the variance
Autocorrelation function is
$$R_{xx}(\tau)=\frac{20}{1+2\tau^2}$$
So at $\tau=0$$$R_{xx}(0)=20=E[X(t)X(t)]=E[X^2(t)]$$ The variance is
$$\mathrm{Var}[X(t)]=E[X^2(t)]-E^2[X(t)]=20-E^2[X(t)]$$ As $X(t)$...
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2answers
234 views
Power spectral density of $\left(x(t)\right)^2$?
The relation between $x(t)$ and output $y(t)$ of a non-linear device is expressed as
$$y(t) = (x(t))^2$$
Let $x(t)$ be zero-mean stationary Gaussian random process with auto-correlation
$$R_x(...
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0answers
85 views
How to preprocess such signals?
I am interested in denoising accerelation measurements, recorded in ambient vibration tests. Such tests consist in recording the vibrations of a mechanical structure, say a table for example. So say I ...
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1answer
37 views
Testing for changes in auto-covariance
I am working with uniformly-spaced time series data where I am interested in knowing whether there are changes in temporal auto-covariance. The mean can be assumed constant. Visually, there are no ...
0
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1answer
773 views
How to estimate the autocorrelation from nonuniformly spaced data
Assume a continues-time random process $X(t)$ sampled nonuniformely in time to acquire discrete signal $x[n]$. The sampling times are known but the autocorrelation is not. Is there an accurate ...
2
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1answer
326 views
Help in interpreting the auto correlation graph
I want to check if a time series is (a) random (b) independent. For these I am using the autocorrelation (AC). Autocorrelation
refers to the correlation of a time series with its own past and future ...
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2answers
1k views
Power spectral density of sinusoidal signal in noise
In a literature I face with this input and power spectral density (PSD)
$$x(t)=s(t)+n(t)=A\cos\left(\omega_c t +\phi\right) + n(t)$$
first I want to know
How can we find PSD of $\cos\left(\omega_c t ...
2
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3answers
4k views
Calculating the fundamental frequency using Autocorrelation often gives half the expected value
I'm currently writing a mobile app which needs to analyse musical notes and find the fundamental frequency to determine the pitch. To do this I'm reading in audio data, taking an FFT, taking the auto-...
1
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1answer
736 views
Does the Wiener–Khinchin-Einstein theorem hold for non-Gaussian processes? If so are there any assumptions?
The Wiener–Khinchin-Einstein theorem states that the auto-correlation $(r_{xx}(\tau))$ and spectral density $(S(f))$ are Fourier duals, i.e.
$$r_{xx}(\tau) = \int^{+\infty}_{-\infty} S(f) \exp\left( ...
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1answer
1k views
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 ...
0
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1answer
437 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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0answers
300 views
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 ...
2
votes
3answers
324 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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2answers
396 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 ...
1
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1answer
640 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 ...
2
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5answers
10k 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
72 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[...
1
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1answer
496 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) ...
4
votes
2answers
309 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
47 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 ...
2
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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
675 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
297 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:
...
0
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1answer
145 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 $...
0
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0answers
340 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 ...
0
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1answer
702 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 ...
2
votes
1answer
739 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 $f_0$, $A$ ...
0
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1answer
214 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 ...
2
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4answers
2k views
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
23 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]...
0
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1answer
554 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
169 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, $P(X[t] = 1) = p$ ...
0
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1answer
209 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 ...
1
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1answer
185 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 ...
12
votes
4answers
2k views
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 ...
-1
votes
1answer
218 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 ...
1
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1answer
271 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 ...
1
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2answers
926 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 ...
0
votes
1answer
535 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 ...
0
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0answers
741 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 $...
