Questions tagged [autocorrelation]
Autocorrelation is the cross-correlation of a signal with itself.
304
questions
0
votes
2answers
36 views
Relation between $X(f)$ and $S_x(f)$
We know that for a signal $x(t)$, it is related to $R_x(\tau)$ as, $$R_x(\tau) = \int_{-\infty}^{\infty}x(t)x(t-\tau)dt$$.
$\\$We also know that $$R_x(\tau) \rightleftharpoons S_x(f)$$
$\\$How do we ...
1
vote
1answer
69 views
Correlation of independent random processes
Suppose $X(t)$ and $Y(t)$ be two independent random processes. Is $E(X(t_1)Y(t_2))$ necessarily zero?
1
vote
0answers
33 views
what is equal to the FT of the Autocorrelation function
I am trying to make my own demonstration in order to find what is equal to the FT of the Autocorrelation function.
The autocorrelation function in some book about turbulence is defined as:
r($\tau$)=...
0
votes
0answers
19 views
Is the expectation of a random process $X(t)$ with zero DC component necessarily zero?
Is the expectation of a random process $X(t)$ with zero DC component necessarily zero? Or can it be non-zero depending upon the process?
2
votes
1answer
48 views
the demonstration that states that the FT of the ACF function is the square of the DTFT of the signal
I am following the book The Intuitive Guide to Fourier Analysis & Spectral Estimation with MATLAB. I am trying to selflearn the fourier analysis in matlab.
I got lost in one passage in the ...
-1
votes
0answers
13 views
Autocorrelation of vector of images
I have a set of images (think a ball getting bigger and smaller). I want to assess the periodicity in this string of images (each data point in my signal is an image). How can I go about doing this in ...
-1
votes
0answers
17 views
What is definition of cross correlation function?
I mean there are three different formulas for cross correlation that I have studied f and g are two functions whose correlation has to be found
1.For Energy signals
2.For Power signals
3.For ...
1
vote
1answer
61 views
Mathematical description of the ACF using fft2
I computed the acf of an image with the following code:
...
2
votes
2answers
105 views
Why is the Fourier (or cosine) transform decorrelating?
The discrete Fourier transform (DFT) and the discrete cosine transform (DCT) both decompose a signal into its frequency-domain spectrum. One property that I have seen praised across various domains ...
0
votes
0answers
17 views
Increasing error safety in the cross correlation of two binary signals in wireless communication
I want to cross correlate two binary signals, where one is corrupted by noise and shifted by a time constant $\tau$, but has the same bit pattern (so basically an auto correlation). Similar to case 2 ...
2
votes
1answer
66 views
What kind of power spectrum implies uncorrelation in time?
I am new in signal processing field, and actually I just need some basic tools for what I am working on. I've learnt that the autocorrelation function is the inverse Fourier transform of the signal's ...
2
votes
2answers
130 views
Autocorrelation of signal with offset
If I have a stationary signal $x(t)$ with zero mean and with an auto correlation $r_{xx}(\tau)$, then what is the auto correlation of $y(t)=x(t)+b$ ?
My calculations so far:
$$\begin{align}
r_{yy}(\...
0
votes
0answers
7 views
After fitting auto ARIMA's order, in prediction I'm getting bad result
For sunspot dataset.
Below is the ARIMA code. Auto ARIMA finds the best ARMA(2,1,2)(2,0,1) model. But when I plot the prediction seems wrong:
...
1
vote
1answer
53 views
How to find the fundamental frequency of a discrete signal using partial autocorrelation?
I hope you can help me with this question.
I am trying to calculate the fundamental frequency (to know the beats per minute) of a cardiac pulse signal using partial autocorrelation.
I use a 12-bit ...
0
votes
1answer
116 views
Autoconvolution vs Autocorrelation
I have a serious doubt about Autocorrelation and AutoConvolution.
My understanding is,
Autocorrelation
Autocorrelation is ...
0
votes
0answers
17 views
Aperiodic Correlation function using FFT Method
Periodic correlation function between two binary sequences say x and y can be computed using FFT. corr_value = ifft(fft(x).*conj(fft(y));
Can some one please help on how to compute aperiodic ...
1
vote
1answer
217 views
Autocorrelation of sinc function
I'm having trouble on computing the autocorrelation of the sinc function
I want to compute
$$R_{hh}(\tau)=\int_{-\infty}^{\infty}\operatorname{sinc}(t) \ \operatorname{sinc}(t-\tau) \ \mathrm{d}t$$
...
1
vote
0answers
38 views
Equivalence of the Power Spectral Density definitions
I am trying to show the equivalence of the following Power Spectral Density definitions in Matlab:
Definition 1:
$$ P(\omega) = \sum_{k=-\infty}^{\infty} r(k)e^{-j\omega k} $$
Definition 2:
$$ P(\...
1
vote
0answers
24 views
How to add noise with given autocorrelation to signal in Matlab?
My question is a mix of signal processing and Matlab coding.
I have an FIR filter with added noise $w_n$ $$x_n=\sum_{m=0}^{N_h-1}h_mg_{n-m}+w_n.$$
Now the noise $w_n$ has the autocorrelation $$E[...
1
vote
0answers
41 views
Zero-padding vs. nonzero-padding in computation of auto-correlation with FFT
Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal?
If I have a measured signal which has good ...
0
votes
0answers
30 views
Autocorrelation function and product of summations
Let $u[k]$ be a white gaussian noise with variance $\sigma^2$ and $y[k]=\sum\limits_{i=0}^q b_i u[k-i]$, that is a moving average model.
I am trying to compute the autocorrelation function of $y[k]$:
...
0
votes
1answer
60 views
Finding period of a square wave with varying sampling frequency
I have a square wave (0-1.8V) with a varying sampling frequency (from a circuit simulator). It is also not a perfect square wave (the high and low signal could be very close to but not precisely zero ...
0
votes
0answers
56 views
Is there an algorithm for computing auto-correlation in a frame-based manner?
I am trying to find out if an algorithm similar to the Overlap-And-Add method that enables frame-based computation of convolution and cross-correlation exists.
When I say frame-based computation I am ...
0
votes
0answers
105 views
Pitch detection, YIN, pYIN
So here is the "seminal" YIN paper:
Cheveigne A, Kawahara H. - YIN, a fundamental frequency estimator
for speech and music
and the new, improved probabilistic YIN:
Mauch M, Dixon S. - PYIN: A ...
0
votes
0answers
38 views
Interpreting Auto correlation results
I used xcorr function in Matlab to compute the autocorrelation of my signal. I obtained a graph, which is shown below. How to interpret this? I read that autocorrelation helps in finding the patterns ...
0
votes
0answers
59 views
On the spectral representation of deterministic and random signals
I went back to many references in order to fix some of the confusions that I have on many concepts in signal spectral representation. I concluded that:
1) Deterministic signals may be represented ...
1
vote
1answer
65 views
Relationship between the autocorrelations of X(t) and X(nt)
Defining:
$X(t)$ WSS random process with autocorrelation function $R_{X}(\tau) = \mathbb{E}[X(t)X(t+\tau)]$.
$Y[n] = X(nT)$ (sampling of $X$ at a rate $\frac1T$) with autocorrelation function $R_Y(\...
0
votes
1answer
48 views
Are there any signals with brickwall autocorrelation?
Are there any signals whose autocorrelation $R(\tau)$ has the following form? Assuming $\tau_c > 0$ and $R_0 > 0$ a constant,
$$R(\tau) = \begin{cases}R_0, \text{ for $|\tau| < \tau_c$} \\ 0,...
3
votes
2answers
131 views
How to find a variance of sample sequence
I have a sequence such as
$$r[n] = y[n]v[n]$$
$y[n]$ and $v[n]$ are zero-mean and statistically independent.
I need to find a variance of $r[n]$ and show that it is white and equal to $\sigma ^2_y\...
0
votes
2answers
64 views
About using Walsh matrix as spreading sequence
I'm asking about some details about using the Walsh matrix as spreading sequence code. For example, suppose I'm using a $4\times 4$ Walsh matrix given by
$$H = \begin{pmatrix}
1 & 1 & 1 & ...
0
votes
1answer
29 views
Particular Correlation formula
I'm reading a book where the autocorrelation of white noise is expressed as:
What is the term $Q(k)$ and why is is expressed as an average value of a dot product ?
1
vote
1answer
39 views
Difference between autocorrelations
M. H. Hayes calls in his book "Statistical digital signal processing" autocorrelation sequences $r[k]$.
For optimal filters the desired autocorrelation has the index d -> $r_d[k]$.
However, often ...
0
votes
2answers
51 views
Correlation between 2 signals of uneven dimensions
As a part of my work, I am trying to correlate the audio signal in a video with the pixels of each frame. The steps I follow are:
Audio sampling rate and frame rate of the video are known. So, ...
2
votes
1answer
73 views
Simulate time series given temporal auto-correlation functions
Given a random process $x[n] \in \mathbb{R}$ (say of length $N$) and all correlation functions such as:
\begin{align}
\langle x[i]\rangle\\
\langle x[i]x[j]\rangle\\
\langle x[i]x[j]x[k]\rangle\\
\...
0
votes
1answer
83 views
Confusion about ensembles and averages in autocorrelation matrices
I just noticed that until now I often don't cared about the scaling of the autocorrelation Matrix in Matlab. I then checked with the book Statistical Digital Signal Processing from M. H. Hayes. There ...
0
votes
0answers
32 views
Autocorrelation
What is autocorrelation in real life? Any example?
How does autocorrelation dependent on time difference? Here is Xt1 and Xt2 how comes \phi{tau}?
0
votes
1answer
595 views
Autocorrelation: numpy versus FFT
I have a series a of values (0 and 1) coming from a Brownian process with drift for which I am studying the autocorrelation.
I used two methods:
1) numpy autocorrelation:
...
0
votes
1answer
88 views
Autocorrelation sequence in terms of Fourier transform of the underlying signal
Let $x(n)$ be a sequence of length $N$, which is zero outside the interval $(0,N-1)$. Let $X(k), k=0,1,\cdots,N-1$ be the FFT coefficients of $x(n)$, that is, $X(k)=\sum_{n=0}^{N-1}x(n) \exp\left( -\...
0
votes
0answers
27 views
Co-prediction of signals
Is there any plausible method to estimate or predict one signal, on the basis of known value of another signal, provided the two signals bear a strong correlation?
For instance, the audio amplitude ...
0
votes
1answer
42 views
Can spectral density be a complex quantity?
I have a signal ($S(t)$) which is product of a Gaussian ($G(t)$) and a random phase function ($e^{i\theta(t)}$, here $\theta(t)$ is a random function), as shown below
$S(t)=G(t).e^{i\theta(t)}$
If I ...
1
vote
0answers
45 views
How to deduce the shape of autocorrelation graphically?
I'm asking for your help in understanding if I have a rectangular function, so the autocorrelation for it will be triangular... and I can prove that graphically but this is time-consuming especially ...
1
vote
0answers
33 views
$E(X(t)X(t))=\sigma^2\delta(\tau)$ or $E(X(t)X(t))=\sigma^2$
(Question already asked on Math StackExchange)
Let's say we have a white noise process $x(t)$ such that:
$E(X(t)X(t+\tau))=N\delta(\tau)$
$E(X(t))=0$
In particular, with $\tau=0$, $E(X(t)X(t))=E(X^...
0
votes
1answer
33 views
Practical insightful time domain functions [closed]
This question might be a little bit different, but i am having hard time to find some sort of a list/book/website/advice, with very practical time domain functions that provides useful insgihts for a ...
0
votes
1answer
49 views
What does a star shaped autocorrelogram mean?
Using the data in the upper graph, I get the weird autocorrelogram of the lower graph:-
I've never seen a autocorrelogram of this shape. They're usually flat along the x axis. Testing the code with ...
0
votes
1answer
15 views
How can faux correlated data be generated for testing or training?
There are one or two questions here that ask how to assess data correlation. The data tends to be empirical.
Is there some tool or standardised technique for generating correlated data from scratch? ...
0
votes
1answer
41 views
Interpolation of missing audio signal in a video sequence
Suppose there is a video sequence and there are some frames for which the audio data is missing. I want to interpolate the missing audio data on the basis of the correlation of the audio signal with ...
0
votes
1answer
193 views
How to determine fundamental frequencies (beats/minute) of heartbeat? (matlab)
read = matfile('ECG.mat');
[cor, lags] = xcorr(read.ecg, read.ecg);
read.Fs;
So i have read.ecg (signal) and ...
2
votes
1answer
35 views
Why is the sound field intensity due to $K$ point sources given by $ I(p,\omega) = \sum_{k=1}^K \sigma_k^2(\omega) \delta(p - p_k)$?
I am trying to understand the following piece of text. I am not used to dealing with sound intensity and power so I'm not familiar with the derivation of the formula $(*)$ below.
Statement: 1.
We ...
0
votes
1answer
130 views
Problem understanding the Expectation Operator
I know that the Expectation Operator $E\{x\}$ four discrete values is
$$ \sum_k \alpha Pr(x = \alpha_k)$$
and its very intuitive when speaking out a formula which contains the Expectation Operator. ...
2
votes
2answers
302 views
How to compute autocorrelation of signal defined by difference equations?
I have no experience with difference equations and I want to learn how to compute the following, but I found no resource online. Any help would be greatly appreciated.
Find:
$$\mathbb{E}\left[d[n]d[...
