Questions tagged [autocorrelation]
Autocorrelation is the cross-correlation of a signal with itself.
0
votes
1answer
34 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, $X(k)=\sum_{n=0}^{N-1}x(n) \exp\left( -\...
0
votes
0answers
19 views
Co-prediction of signals
Is there any plausible method to estimate or predict one signal, on the basis of known value of another signal, provided the two signals bear a strong correlation?
For instance, the audio amplitude ...
0
votes
1answer
31 views
Can spectral density be a complex quantity?
I have a signal ($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 ...
0
votes
0answers
17 views
Autocorrelation graphically deduce
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 ...
0
votes
0answers
8 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 ...
1
vote
0answers
26 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^...
-1
votes
0answers
20 views
Autocorrelation after sampling - Random Process
I hope someone can help me with the following problem:
Given a zero-mean complex white Gaussian noise process $n(t)$ I first calculate the autocorrelation $R_n(\tau)$.
The real and imaginary part ...
0
votes
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
votes
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
votes
0answers
8 views
Imposing constraints in mixture modeling of correlated data?
For 1-D signals (spectra) or 2-D signals (images), is there a way to impose the constraint that the data within a group is uncorrelated? I am iteratively applying background correction model fitted to ...
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
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
65 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
votes
1answer
38 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
209 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
52 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
38 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
0answers
17 views
Correlation between elements of a video
Should there be an expected correlation between the audio signal and the frame pixel data, considering the frames of a video?
If so, what is the reason for such correlation? Pondering over the topic ...
0
votes
1answer
47 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
votes
0answers
18 views
Wiener Filter: spacing of the data
I read in an article that for the discrete version of Wiener filter as proposed by Levinson, the data can be arbitrarily spaced. What is implied by this? I believe that the spacing does matter to ...
0
votes
1answer
30 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
49 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
98 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 ...
1
vote
2answers
126 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
votes
1answer
57 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
votes
1answer
59 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 ...
1
vote
2answers
55 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 ...
0
votes
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}, ...
0
votes
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 ...
2
votes
2answers
66 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 ...
0
votes
0answers
26 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 ...
0
votes
0answers
18 views
On the confidence intervals of matrix autocorrelation
Considering the case of signal autocorrelation in 1D, I've read that the distribution of the correlation coefficients $r$ of a white noise (independent and identically distributed random variable) ...
2
votes
1answer
106 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
votes
0answers
101 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 ...
1
vote
0answers
64 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
59 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
votes
0answers
74 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):
$$...
-1
votes
3answers
106 views
The explanation of $|R_{XY}(\tau)| \le \sqrt{R_{XX}(0)R_{YY}(0)}$
If i said the explanation of $|R_{XX}(\tau)| \le R_{XX}(0)$ is that in the time domain,any signal wave are the same as itself when it doesn't shift.Then what is the explanation of $|R_{XY}(\tau)| \le ...
0
votes
2answers
44 views
Synchronization with a specified sequence
I'm currently creating a project in Matlab where I'm simulating a communication, based on the SSB modulation, between a transmitter and a receiver.
I've added a Barker sequence in the trasmitted ...
1
vote
1answer
32 views
Null autocorrelation function and stationary
I can show that a process $X(t)$ is Wide Sense stationary (WSS) by showing that $E[X(t)]$ is constant and that its autocorrelation function is in function of $\tau=t_1-t_2$, that is, $R_X(t+\tau,t)=...
3
votes
2answers
114 views
Auto-correlation function, an inverse problem
$x[n]$ is a complex function $n=0,1,2,\cdots,L-1 $
we assume $x[n]$ is periodic in its index: $x[n+L]=x[n]$
Its auto-correlation function $C[n]$ is uniquely defined as:
$$
C[n]=\sum_{i=0}^{L-1} x[i+...
0
votes
1answer
105 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 $:
$$ Z (t) = aX(t) +...
0
votes
2answers
175 views
Ornstein Uhlenbeck with drift
The Ornstein-Uhlenbeck (OU) process
$dX_t = -\frac{1}{\mu} X_t + \sqrt{\frac{2\sigma^2}{\mu}} dW_t $
generates coloured noise with autocorrelation function $R(t) = \langle X_t,X_{t'}\rangle = \...
1
vote
2answers
143 views
Harmonics to Noise Ratio Estimation
I'm willing to estimate the Harmonics to Noise Ratio (HNR) of a speech signal x[k] and using autocorrelation method.
Theoretically, HNR is given as,
$\ HNR = \frac{R_{xx}[T_0] }{R_{xx}[0]-R_{xx}[...
2
votes
2answers
102 views
Interpreting this plot cross-correlation
I have an input signal $x(t)$ that is a white Gaussian random signal with mean 0 and variance 1. The signal $y(t)$ is the output of a linear filter with impulse response $$h(t) = |\operatorname{sinc}(...
0
votes
2answers
48 views
Calculation of autocorrelation - does calculation “loop”?
With a delay $l$, autocorrelation is defined as:
$$r_{xx}(l) = \sum_{n=-\infty}^{\infty}x(n)x(n-l) = \sum_{n=-\infty}^{\infty}x(n)x(n+l).$$
I want to calculate the autocorrelation of a signal
$$x(n)...
0
votes
0answers
58 views
Autocorrelation Matrix of a AR process
i'm beggining to study signal processing, and i'm having trouble on writting it ( specially defining the signal x(n) ) in matlab and finding the solution for this problem, if anyone could help I would ...
0
votes
0answers
37 views
Computing Power spectral Density
Acronyms: Power spectral density, PSD
Autocorrelation, AC
Hey so I'm in my first ever DSP class and thoroughly enjoy the material, but absolutely suffer in the HW. I have this question ...
