Autocorrelation is the cross-correlation of a signal with itself.
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1answer
34 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 ...
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0answers
20 views
How is PACF analysis output related to LSTM?
I was going through a recent paper “A Novel Hybrid Data-Driven Model for Daily Land Surface Temperature ForecastingUsing Long Short-Term Memory Neural Network Based on Ensemble Empirical ...
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0answers
29 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, ...
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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 ...
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1answer
38 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 ...
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16 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 ...
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1answer
25 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 ...
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0answers
10 views
Cut two signals from a correlated signal
I have the following situation, I did ACF auto correlation between temperature and strain. I got a shifted signal in temperature and I already shifted it.
Of course the shifted signal has shorter ...
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2answers
44 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 ...
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1answer
49 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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2answers
70 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 ...
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1answer
33 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_{...
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1answer
42 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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2answers
42 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
17 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
20 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
58 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
24 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 ...
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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
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1answer
67 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 ...
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0answers
59 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
57 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 ...
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1answer
45 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)|} $$
where $C$ is a compression function like bz2 or zip, ...
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68 views
ACF and impulse response
These are questions according to the system identification.
I can understand some questions:
Is there a relation between autocorrelation function and impulse response?
Is it possible to identify the ...
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1answer
40 views
Auto-correlation of the sum of two generic signals
Be $x[n]$ and $y[n]$ two generic discrete-time signals. Given $s[n] = x[n] + y[n]$ I want to evaluate its autocorrelation $R_s[l]$.
By definition (https://en.wikipedia.org/wiki/Cross-correlation):
$$...
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3answers
98 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 ...
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2answers
39 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
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1answer
29 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
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2answers
104 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:
$$
C[n]=\sum_{i=0}^{L-1} x[i+...
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1answer
70 views
Autocorrelation of Addition of Two Independent Signals
Given a random signal $ Z \left( t \right) $ which is addition of two independent signals $ X \left( t \right) $ and $ Y \left( t \right) $ with constant parameters $ a $ and $ b $:
$$ Z (t) = aX(t) +...
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2answers
93 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 = \...
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2answers
95 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}[...
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2answers
89 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 $$h(t) = |\operatorname{sinc}(...
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2answers
39 views
Calculation of autocorrelation - does calculation “loop”?
With a delay $l$, autocorrelation is defined as:
$$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)...
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0answers
41 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 ...
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0answers
33 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 ...
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1answer
32 views
Is there a closed form solution for a temporal calibration of two different signals?
Given two signals $f_1(t),f_2(t+dt)$ where $t$ is time and $dt$ is the time delay between the two signals,
is there any closed-form solution with respect to $dt$?
what are the efficient global ...
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0answers
20 views
Correlation of the amplitude and angle, and various modulations
I am trying to determine if a signal exists at a frequency by sampling, shifting and downsampling (to get the baseband), and autocorrelating the result. The signal is IQ samples from an SDR.
I have ...
2
votes
2answers
158 views
Autocorrelation of discrete signal $\sin{2\pi fn}$
Determine the autocorrelation $r_{xx}[m]$ of the discrete signal
$$x[n] = (\sin2\pi fn).$$
where $n$ and $m$ are integers.
Using the definition I get
$$\begin{align}
r_{xx}[m] &= \...
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0answers
15 views
computing auto correlation for some images
would you please help me how to compute auto correlation for some images (in the form of some 2D matrices)?
for example, how can I compute auto correlation for these 3 matrices manually?
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2answers
70 views
Derivation of $ R_{N(t)}(\tau) $ from its $f_{N(t)}(\eta)$
How can we prove the auto-correlation function of white gaussian noise $\{ R_{N(t)}(\tau) \}$ is $\frac{N_0}{2} \delta(\tau)$ from its p.d.f in equation below?
$$
f_{N(t)}(\eta)=\frac{1}{\sqrt{2 \pi \...
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2answers
75 views
How to calculate time of arrival using room impulse response
I need to find the timestamp of arrival of a particular signal at a receiver location within a room. The known parameters are the room impulse response h for a ...
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1answer
33 views
Finding number of independent samples using autocorrelation
I have a pressure signal (y) with 512000 samples and with a sampling frequency ...
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2answers
92 views
Autocorrelation of a Shifted Sequence
Suppose I have a sequence $x[k]$ with $\mathcal{Z}$-transform
$$ X(z) = x_{0} + x_{1}z^{-1} + x_{2}z^{-2} + \ldots + x_{N-1}z^{N-1}$$
I know that for real-valued $x[k]$ the $\mathcal{Z}$-transform ...
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0answers
83 views
Average of autocorrelation functions
Let $X$ and $Y$ are two non-random time series of length $N$ with $\rho_i^{xx}$ and $\rho_i^{yy}$ are the autocorrelation functions of lag $i$, respectively. What is the autocorrelation function of $Z$...
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1answer
76 views
Doubt about wide sense stationary random process
I have white Gaussian noise $F[n]$ with zero mean and autocorrelation $R_F[n_1,n_2]=\delta[n_1-n_2]$.
If now I consider the random process defined as
$$X[n]=u[n]e^{-kn}F[n]$$ Is $X[n]$ a wide-ense ...
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1answer
484 views
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55 views
Autocorrelation BPSK Transmit with Binary Sequence (PRN Code)
I am working to design the Transceiver using a SDR hardware. In the transmitter side, the BPSK modulation was used to modulate a binary sequence number which has good autocorrelation properties. The ...
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0answers
34 views
what is the relation between autocorrelation lags and fundamental frequency?
I am studying autocorrelation based feature paper. In that they extracted autocorrelation feature and after that they plotted graph lags vs fundamental fundamental frequency...I am not getting ...
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1answer
342 views
proof of Autocorrelation property of DFT
I am facing problem in proving the Auto-correlation property of Discrete Fourier Transform (DFT), that is
$$\mathcal{DFT}\left\{\sum_{r=0}^{N-1}x[r]x^*[r+n]\right\} = X[k]X^*[k]= |X[k]|^2$$
where $X[...
