Questions tagged [autocorrelation]
Autocorrelation is the cross-correlation of a signal with itself.
388
questions
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1answer
67 views
Symmetries of analyticity / zero self-correlation
I seek to understand symmetry properties of analytic sequences, without referring to frequency domain: what criteria must a complex sequence $x[n]$ satisfy to be analytic? Framed alternatively, such a ...
1
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1answer
46 views
How this convolution integral is solved to obtain autocorrelation function of current for shot noise?
I am studying shot noise characteristics from this source:
Here the author writes that autocorrelation function is given by:
$$R_I(\tau)=\bar{h}*h*R_Z(\tau)$$
where $R_Z(\tau)=q^2(\lambda^2+\lambda \...
0
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1answer
23 views
Relation between bandwidth and amplitude of auto correlation of chirp signal
I am trying to understand the properties of chirp signals and their characteristics.
I plotted the autocorrelation of a chirp signal in MATLAB.
How can I compute the relation between the amplitude of ...
0
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2answers
30 views
Should upsampling impact the amplitude of an autocorrelated signal?
I want to autocorrelate a signal using numpy's correlate method.
Let us consider a 10 minutes long signal sampled at 2,000SPS:
...
0
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1answer
49 views
Restrictiveness of the condition that different signals give same autocorrelation sequence
I'm having a set of N real data points that correspond to the autocorrelation sequence at N different lags. Suppose I know that the original set of data from which the autocorrelation was computed ...
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0answers
63 views
Create a Range Doppler Map using “Arbitrary” phase coded Waveforms
This is my first questions I am asking to this community!
I want to understand how to create a Range-Doppler Map (RDM) for a phase/frequency coded radar return using an arbitrary waveform generator (...
2
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1answer
48 views
Method to generate binary sequences with desired cross-correlation and autocorrelation properties
I am looking for a method to generate two binary sequences of length $N$ with the following properties:
Very good cross-correlation for all shifts.
Good enough autocorrelation for all shifts except ...
1
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1answer
171 views
Allan Variance vs Autocorrelation - Advantages
I am currently studying oscillator stability and have come across the Allan variance. I gather that it was developed as an alternative to the standard variance as it doesn't necessarily converge for ...
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0answers
19 views
How to select the ARMA model parameters?
I have a series of data containing 120,000 points. The mean of each N(=60) point is zero. I want to forecast the next 60 points using the ARMA model. My question is, specificaly, how to choose the ...
1
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1answer
159 views
Extremes of integral of the autocorrelation theorem
I am trying to apply the correlation theorem (here attached) to this definition of correlation of a finite continuous signal $g(t)$:
$\rho(\tau)=\frac{1}{T} \int_{t_{0}}^{ t_{0}+T}g(t)^{.}g(t+\tau)dt ...
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0answers
31 views
Question about a demonstration of the autocorrelation theorem
I’m stuck on this demonstration.
It says:
If $x'$ is held constant, $dx=dy$
How can $x’$ be constant? Shouldn't $x’$ be a variable?
2
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1answer
86 views
Isolate g(t) starting from the definition of power spectrum
Starting from the following definition of power spectrum of a signal $g(t)$ in time:
$$S(f)=\int_{-\infty}^{+\infty}\rho(\tau)e^{-i2\pi f \tau} d\tau$$
where
$$\rho(\tau)=\int_{-\infty}^{+\infty}g(t)^{...
1
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1answer
53 views
Expected Value of a sequence with two random variables
If I have a signal of the form $x\left(n\right)=Acos\left(nω+ϕ\right)$
where
$\omega \in \left[\omega -\lambda ,\omega \:+\lambda \:\right]$ is a uniform random variable
and
$\phi $ is also a uniform ...
0
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0answers
13 views
Calculate ACF in C++?
I would like to manually reproduce the method that authors of an article used in their research (DOI: 10.1038/s41598-017-02750-9 (Page 8. top)). It is mentioned as "ACF", so I wrote ...
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0answers
29 views
Signal “seasonality” detection
I am wanting to do a seasonality detection on a signal, but am struggling big time to find a solution.
I have tried several different things, including statsmodels STL/seasonal_decompose. It seems ...
0
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1answer
53 views
autocorrelation of multiple signals
Problem: I am looking at an adaptive filtering application where the eigenvaluespread of the autocorrelation matrix $R$ is important for the convergence of the algorithm. For a single channel system ...
2
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0answers
66 views
Ringing/Oscillation in the reconstructed Periodogram
I have an original periodogram that I need to model with autoregressive process. However the model isn't right as it is not fitted well to the original periodogram.
I am suspecting I am doing ...
0
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2answers
81 views
Processes/Transforms involved to get brainwave data from raw EEG? (Autocorrelation confusion)
Not clear on what the autocorrelation function of raw EEG means physically
why can't you take the FT of a the EEG itself and get frequency data?
With BCI & basic electrode setups you can ...
0
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1answer
153 views
Find the autocorrelation function of signal $x(t) = u(t) - u(t-1)$
I have used the energy-type signal autocorrelation function:
$$\mathcal{R}_{xx}(\tau)=\int_{-\infty}^{\infty}x(t)x^*(t+\tau)dt$$
I have rewritten the equation as:
$$\begin{align}
\int_{-\infty}^{\...
1
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2answers
115 views
How to find the output mean and autocorrelation of a non-linear system
I need help with this question. I am sure this is the right StackExchange forum for this type of question.
Consider a nonlinear device such that the output is $Y(t) = aX^2(t)$, where the input X(t) ...
0
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0answers
35 views
Cross-correlation estimation in MATLAB using a method similar to pwelch for the PSD
Is there a function in MATLAB to estimate the cross correlation function of two wide-sense stationary signals (or the autocorrelation of the signal with itself) in a way similar to the estimation of ...
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0answers
28 views
Generating data with given Auto and Cross Correlations
I have two discrete vectors $\mathbf{x}_1$ and $\mathbf{x}_2$, and I'm trying to generate more data $\mathbf{f}_1$ and $\mathbf{f}_2$ that has some basics properties of $\mathbf{x}_1$ and $\mathbf{x}...
1
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1answer
66 views
What are some really accurate ways to get the value of a peak (local maximum) given some points around it? (To be used for autocorrelation peaks.)
I have looked everywhere on the internet for this and, surprisingly, haven't found much useful information.
Given 3 or more points closest to a peak (local maximum) what are some of the most accurate ...
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1answer
351 views
Autocorrelation function of a triangular wave
I am interested to find the analytical expression for the autocorrelation function of a signal that comprises triangular pulses. I have followed the derivation in "Statistical Theory of ...
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0answers
88 views
Calculate periodicity of audio signal
I have to calculate the periodicity of a audio signal like this:
You can see by eye, that the volume rises the highest every second "blob".
The spectogram (that is visualized ...
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0answers
39 views
Auto-correlation of absolute squared stochastic process
Consider the stochastic process $a(t) \in \mathbb{C}$. Its autocorrelation function is given as
$$
\phi_{aa}(\tau)=\left(a(t)\star a(t)\right)(\tau)=\int_{-\infty}^{\infty}a^*(t)\cdot a(t+\tau) \...
3
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1answer
132 views
Prove that a specific auto-correlation function is even
Background (from digital signal processing):
The $\delta$ function is defined as below:
$$\delta[n]=\begin{cases}
1 \quad \mbox{if} \hspace{.4em} n=0\\
0 \quad \mbox{o.w.}
\end{cases}$$
In an LTI (...
0
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0answers
36 views
How to compute autocorrelation with exponential IIR filter efficiently
I have a discrete dataset (called V). I want to compute the autocorrelation of V at multiple time horizons. Normally I know that I can use the IFFT of the PSD. But in my case I need it with ...
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0answers
40 views
How to apply the window function when finding autocorrelation?
I want to get frequencies from amplitudes and I'm following Chap 5.1.1 from Speech Signal Processing by Praat
As the in pictures, I will multiply the signal $s(t)$ with the Hanning window $w(t)$, ...
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0answers
33 views
PSD of linearly modulated signal using autocorrelation?
Consider a signal $v(t)$ given by
$$v(t)=\sum_{n=-\infty}^{\infty} b[n]p(t-nT).$$
Assume that $b[n]$ is uncorrelated with zero mean, i.e. $\mathbb{E}[b[n]b^*[m]]=\mathbb{E}[|b[n]|^2]\delta[n-m]$ and $\...
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0answers
26 views
Calculation of eigendecomposition of a signal in its Fourier domain?
I want to find the eigendecomposition of a 3-dimensional discretely sampled signal $X$, where each sample $X_{i,j,k}$ is treated as a vector $\langle i, j, k\rangle$ (with the origin at the middle of ...
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2answers
460 views
Autocorrelation for periodic signals
Autocorrelation for power signals is defined by $$R_x(\tau)=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^Tx(t)x^*(t-\tau)dt\tag{1}$$ Is it true that for periodic signals $(1)$ can be computed by $$R_x(\tau)=...
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1answer
92 views
How is time used in this autocorrelation expression?
There are two papers I'm working through that explain applications of autocorrelation.
The first - by Monti - is quite clear to me:
It runs a sum over the time axis.
The second one by Brown makes no ...
0
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0answers
61 views
finding power spectral density from a vector
I have been given a vector:
\begin{equation}
v= \:\begin{pmatrix}\frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix}
\end{equation}
my job is to find the power spectral density from this vector
\...
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0answers
127 views
Estimating Signal-To-Noise ratio from discrete time series
A hidden variable $x(t)$ (in my case, neuronal signal averaged over a brain area) exhibits dynamics on multiple timescales from milliseconds to seconds. An observable $y(t)$ is produced by convolving $...
0
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1answer
113 views
Computing Autocorrelation via FFT
I have seen several methods to calculate Autocorrelations using FFTs, and am confused about why they differ.
Zero-Pad it to double its original length.Take the FFT. Then replace all the coefficients ...
1
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1answer
208 views
Proving the upper bound of cross correlation
I am reading about cross-correlation from this document and equation (5) states that
The maximum value of the crosscorrelation is not always when the shift
equals zero; however, we can prove the ...
0
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0answers
27 views
Self-correlation vs Digital frequency: figure from paper
In the paper, is discussed a MIMO-OFDM system over the frequency self-correlation of i.i.d. Rayleigh
channels and subcarrier grouping. in this paper is shown the following figure.
it shows the self-...
1
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1answer
66 views
What's the relation between frequency band of $X(j\omega)$ and $\Phi_{xx}(j\omega)$?
in which:
$x_{c}(t)$ is a continuous-time signal
$X(j\Omega)$ is the Fourier Transform of $x_{c}(t)$
$\Phi_{xx}(j\Omega)$ is the Power Spectrum Density of $x_{c}(t)$ which defined as Fourier ...
1
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1answer
72 views
auto-correlation of differentiator
How to do this entirely in the time-domain, without using frequency domain?
Let's say I have a continuous-time system that is a differentiator, and X(t) is WSS:
$$x(t) \rightarrow \boxed{\frac{d}{dt}} ...
3
votes
2answers
467 views
Power Spectral Density from Probability Density Function
The samples of a signal $x[n]$ are i.i.d. and follow a triangular pdf with $a = 0,\ b = 2,\ c = 1$:
The DC-power of the signal is
$$\mu_x^2 = \big(\mathbb{E}(X)\big)^2 = \left(\int_{-\infty}^{\infty} ...
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0answers
54 views
correlation matrix vs. correlation function?
Can someone help me understand the difference between a 1-dim autocorrelation function and a 2-dim autocorrelation matrix of a random process aka time series?
My Leon-Garcia textbook defines CX(τ) and ...
0
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1answer
25 views
Are ACF plots sufficient to detect white noise assuming probable existence of non linear associations?
ACF plots use autocorrelations tests to determine associations in time series. Autocorrelations, however, only measure linear associations. To my understanding, certain non-linear associations can ...
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0answers
31 views
aperiodic auto correlation properties
I'm reading about PSC (primary synchronization code) in UMTS. It is a so-called Golay sequence.
It is said it has a good aperiodic auto correlation properties.
What does it mean (in terms of aperiodic)...
2
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0answers
64 views
Autocorrelation not as expected
I am trying to find the autocorrelation function on the intensity of a pixel over time stored in an array "Intensity". Usually one would expect the highest point to be at t = 0 and then decay. I am ...
1
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2answers
128 views
Discrete-time sampling of filtered white noise
I am trying to understand how I can relate a discrete-time random process to a continuous-time random process sampled at discrete times.
Suppose I have a noise source $N_\tau(t)$ which is derived ...
0
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3answers
798 views
Autocorrelation function and correlation integral
I am confused by the definition of autocorrelation function. It is originally defined as the expected value
$$R_{XX}(\tau) = E[(X(t)X(t+\tau)] = \langle X(t)X(t+\tau)\rangle\tag{1}$$
where $\langle\...
1
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1answer
64 views
Evaluating discrete spectral density at only a few frequencies
I'm trying to obtain the spectral density at three particular frequencies for a computational chemistry problem that I'm working on (if you are curious, it has to do with the estimation of Nuclear ...
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0answers
55 views
Calculation of channel autocorrelation for LMMSE
I am currently trying to implement an LMMSE estimator/equalizer for a python based ofdm receiver. The actual reception is done with a SDR and iq-samples are stored in a file for the "ofdm-receiver" ...
0
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1answer
115 views
Blackman-Tukey Autopower equation
I am looking over Blackman-Tukey method for Autopower.
It uses the DFT after a window is applied on a autocorrelation.
$$
Power Spectrum = \frac1{2\pi} \ \sum_{(k=-(N-1))}^{N-1} w[k] R[k] e^{-i\...
