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Autocorrelation is the cross-correlation of a signal with itself.

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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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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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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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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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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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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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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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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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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) ...
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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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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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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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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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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 ...
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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)=...
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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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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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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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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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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 ...
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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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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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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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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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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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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[...