Questions tagged [autocorrelation]
Autocorrelation is the cross-correlation of a signal with itself.
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2answers
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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
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2answers
59 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 & ...
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1answer
15 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 ?
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1answer
31 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 ...
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2answers
39 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
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1answer
63 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
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1answer
43 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 ...
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0answers
25 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}?
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1answer
77 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
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1answer
42 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( -\...
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0answers
22 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 ...
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1answer
35 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 ...
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0answers
33 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 ...
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0answers
15 views
Computer Vision - What are the possible values for indices in auto correlation function for Harris Corner Detector?
The auto correlation function for Harris Corner Detector is defined as
$E(u, v) = \Sigma_{x, y} w(x, y) [I(x + u, y + v) - I(x, y)]^ 2$
The idea here is that we ...
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0answers
28 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
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1answer
32 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
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1answer
46 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
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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
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1answer
27 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
89 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
33 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
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1answer
50 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)$$
and its very intuitive when speaking out a formula which contains the Expectation Operator. ...
2
votes
2answers
220 views
How to compute autocorrelation of signal defined by difference equations?
I have no experience with difference equations and I want to learn how to compute the following, but I found no resource online. Any help would be greatly appreciated.
Find:
$$\mathbb{E}\left[d[n]d[...
0
votes
1answer
53 views
Correlation of a signal
I have one sample for a signal. This sample is a vector of length 384. I need to calculate the correlation matrix for this signal,So I need many samples for the same signal.
How can i generate these ...
2
votes
0answers
39 views
How to visualize the autocorrelation matrix and it's properties
Having a hard time wrapping my head around autocorrelation matrix as it applies to a spectral estimation problem like MUSIC or ESPRIT. If the signal vector contains a summation of sinusoids in noise, ...
0
votes
1answer
49 views
Fluctuation of autocorrelation of a signal due to signal's noise
I have a question about the fluctuation of autocorrelation of a signal due to signal's noise.
I have a signal defined in $-1\leq t \leq 1$ as the following:
$V(t)=kt+R(t)$, where $R(t)$ is the random ...
0
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1answer
31 views
Question on Levinson's proposed discrete form of Wiener filter
The whole foundation of Levinson's discrete version of Wiener filter is based on the assumption of stationarity of a time series, and aims to predict a value based on the past observed values. Now, if ...
2
votes
2answers
50 views
Finding the auto-correlation sequence $r_{xx}[k]$ for an AR(2) process
Consider the following recursive difference equation of a LTI system, where $v[n]$ is a white noise, zero-mean process with $\sigma_v^2 = 1$.
$
x[n] = v[n] + 0.75x[n-1]-0.25x[n-2]
$
I want to ...
1
vote
1answer
154 views
Confusion about PSD and RMS
Let's say I have a noise power-spectral-density (PSD) which is not flat and ranges from 0 to $f_1$ Hz in frequency. As we know, the total area under the PSD is equal to the total average power of the ...
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vote
2answers
157 views
Does the auto-correlation function of stationary random process always converge?
The auto-correlation function of the stationary random process only depends on the time difference $\tau$.
http://web.ntpu.edu.tw/~yshan/chapter6_han.pdf
64th slide of this lecture note mentions ...
0
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1answer
74 views
Wiener Filter in Frequency Domain: What it does to a specific Frequency?
As I understand Wiener filter in time domain tries to estimate a signal as close as possible to its (original) non-degraded signal using the degraded signal by white noise.
$$H(\omega)=\frac{\Phi_{...
0
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1answer
75 views
While finding the ESD/PSD of a signal why we always prefer to find it via Auto-correlation function then the square of the FT of the signal? [closed]
In a video i saw that while calculating ESD or PSD of a signal time auto correlation function was used when it can be also done by the square of FT of the signal.Why we followed that approach even ...
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vote
2answers
57 views
Image Interpolation Using the Yule Walker Equations
I have been studying about the Yule-Walker equations for prediction of a time series data from knowledge of past values of the series. Is there any way I can use the same in an image to exploit the ...
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0answers
19 views
Positive definites of correlation functions
Say I you have two time series, $x_k, k=1,2$ generated from two, possibly correlated, complex gaussian processes. The lag 0 and 1 auto-correlation estimate for the two time series is denoted $R_{0,k}, ...
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1answer
22 views
detection of periodicities in n-dimensional signals
Generally speaking, what analyses are necessary and sufficient for the detection of periodicities in an n-dimensional signal amounting to a discretely sampled density distribution over n-dimensional ...
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2answers
74 views
Why use $\chi^2$ test to determine the presence of white noise?
I want to test for the presence of broadband noise in a snapshot 1000 complex baseband samples recorded by a software defined radio.
As a follow-up to this post, why was the $\chi^2$ test used? How ...
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0answers
27 views
Time Series Extrapolation from existing past values
Using the Levinson-Durbin algorithm, I am trying to predict the next value in a time series based on previous observations, but the results do not follow the trend of the time series. How can I ...
2
votes
1answer
128 views
Linear Predictive coding vs AR modeling
I'm looking for a suitable explanation of the circumstances in which the LPC error polynomial for a discrete time process x[n] is replaceable with an error polynomial categorized under the AR model? I ...
0
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0answers
118 views
Matrix cross correlation in python
I'm currently performing matrix cross correlation in python using :
C = scipy.signal.correlate2d(A,A)
where A is a 2D matrix, typically a picture. As you can ...
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0answers
65 views
Subtracting audio signal emitted - trying to use spectral subtraction to localize moving objects
I am a Software Engineer without much signal processing background and currently spending and experimenting to get use to it.
My scenario: Assume a speaker and a microphone array. A speaker emits an ...
1
vote
1answer
68 views
What exactly does compression say about correlation of data?
I've been using the following formula on various empirical data $d$, to obtain a correlation factor $c_f$:-
$$ c_f = { |C(d_s)| \over |C(d)|} $$
where $C$ is a compression function like bz2 or zip, ...
0
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0answers
77 views
ACF and impulse response
These are questions according to the system identification.
I can understand some questions:
Is there a relation between autocorrelation function and impulse response?
Is it possible to identify the ...
0
votes
1answer
41 views
Auto-correlation of the sum of two generic signals
Be $x[n]$ and $y[n]$ two generic discrete-time signals. Given $s[n] = x[n] + y[n]$ I want to evaluate its autocorrelation $R_s[l]$.
By definition (https://en.wikipedia.org/wiki/Cross-correlation):
$$...
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votes
3answers
113 views
The explanation of $|R_{XY}(\tau)| \le \sqrt{R_{XX}(0)R_{YY}(0)}$
If i said the explanation of $|R_{XX}(\tau)| \le R_{XX}(0)$ is that in the time domain,any signal wave are the same as itself when it doesn't shift.Then what is the explanation of $|R_{XY}(\tau)| \le ...
0
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2answers
45 views
Synchronization with a specified sequence
I'm currently creating a project in Matlab where I'm simulating a communication, based on the SSB modulation, between a transmitter and a receiver.
I've added a Barker sequence in the trasmitted ...
1
vote
1answer
32 views
Null autocorrelation function and stationary
I can show that a process $X(t)$ is Wide Sense stationary (WSS) by showing that $E[X(t)]$ is constant and that its autocorrelation function is in function of $\tau=t_1-t_2$, that is, $R_X(t+\tau,t)=...
3
votes
2answers
120 views
Auto-correlation function, an inverse problem
$x[n]$ is a complex function $n=0,1,2,\cdots,L-1 $
we assume $x[n]$ is periodic in its index: $x[n+L]=x[n]$
Its auto-correlation function $C[n]$ is uniquely defined as:
$$
C[n]=\sum_{i=0}^{L-1} x[i+...
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1answer
137 views
Autocorrelation of Addition of Two Independent Signals
Given a random signal $ Z \left( t \right) $ which is addition of two independent signals $ X \left( t \right) $ and $ Y \left( t \right) $ with constant parameters $ a $ and $ b $:
$$ Z (t) = aX(t) +...
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2answers
210 views
Ornstein Uhlenbeck with drift
The Ornstein-Uhlenbeck (OU) process
$dX_t = -\frac{1}{\mu} X_t + \sqrt{\frac{2\sigma^2}{\mu}} dW_t $
generates coloured noise with autocorrelation function $R(t) = \langle X_t,X_{t'}\rangle = \...
1
vote
2answers
161 views
Harmonics to Noise Ratio Estimation
I'm willing to estimate the Harmonics to Noise Ratio (HNR) of a speech signal x[k] and using autocorrelation method.
Theoretically, HNR is given as,
$\ HNR = \frac{R_{xx}[T_0] }{R_{xx}[0]-R_{xx}[...
