Questions tagged [autocorrelation]
Autocorrelation is the cross-correlation of a signal with itself.
451
questions
1
vote
1
answer
47
views
Power Spectral Density and Total Power Calculation for Signal
I am currently working on analyzing a signal with the autocorrelation function given by:
$$R(\tau) = 100 \cos( 10000\pi\tau) (Λ(2000\tau))^2$$
I need assistance in plotting the power spectral density ...
1
vote
1
answer
51
views
Frequency content of a noisy signal
To find the frequency content of a noisy signal (PSD), there are two methods below:
#1 Take the fourier transform of its power signal (square the noisy signal)
#2 Find the autocorrelation function of ...
- 21
0
votes
0
answers
29
views
finding Channel Impulse Response using GNUradio and USRPs
I would like to share my project where I am calculating the Channel Impulse Response using the Auto-correlation Method in the Time domain. I have uploaded a video demonstrating the experiment, ...
- 1
1
vote
1
answer
40
views
Finding mean, autocorrelation, and power spectrum of $y[n]=(x∗h)[n]$ where $x[n]$ is zero mean white gaussian noise
If given $x[n]$ is zero mean white Gaussian noise with variance $\sigma_x^2$, and a filter with a known impulse response $h[n]$, how would I find the mean, autocorrelation, and power spectrum of $y[n] ...
3
votes
1
answer
219
views
What's the exact definition of the power spectral density function?
I learned from my signal processing course that PSD is the Fourier transform of the autocorrelation function.
$$\mathscr{F}\Big\{\mathrm{E}\big[x(t)x(t+\tau)\big]\Big\}$$
Today I took my statistic ...
- 33
1
vote
0
answers
40
views
Autocorrelation-properties
How do we go about proving the property that entails; If X(t) is ergodic with no periodic components the autocorrelation converges to square of the mean as the time difference(τ) approaches infinity
𝝁...
- 11
1
vote
1
answer
132
views
Proving that the autocorrelation of a signal is the convolution with its time-reversed complex conjugate
I need to prove the property $$f(x)⊕f(x)=f(x)⊗f^*(-x)$$ That is the autocorrelation of a function is the convolution with its time-reversed complex conjugate. I have constructed most of the proof but ...
- 19
0
votes
1
answer
47
views
Why is power level area under the autocorrelation function of the white-noise signal?
A paper I am reading (Linear and Nonlinear Encoding Properties of an Identified Mechanoreceptor on the Fly Wing Measured with Mechanical Noise Stimuli) defines power level for a white-noise signal as ...
0
votes
0
answers
17
views
Confusion with Complex Gaussian process with Auto-covariance
I have a complex sequence $z(t)$ in time which I know to be a Gaussian process. I read that the complex Gaussian process is not only characterized by the covariance, but also the pseudo-covariance ...
- 107
1
vote
0
answers
41
views
Input (Auto)Correlation Matrix for LMS Adaptive Algorithm
I read quite a few posts regarding the autocorrelation matrix and although some of them were of the LMS adaptive algorithm application, I didn't find an answer to my question.
How do I calculate R; ...
- 11
1
vote
1
answer
104
views
Inferring properties of a signal from its autocorrelation
In a previous thread, it was asked whether we can infer a signal from its autocorrelation, and the answer was a clear no, since the autocorrelation process is lossy.
Still, is there anything we can ...
0
votes
1
answer
78
views
Autocorrelation: why is the lagging necessary?
I am currently studying for my last exam.
I wanted to ask why it is necessary or useful to perform the autocorrelation of a signal with a lagged version of itself
Why does it have to be lagged?
- 1
2
votes
1
answer
430
views
How is the PSD the Fourier Transform of the Autocorrelation function?
I am getting very confused with the textbook I am reading through: Modern Digital and Analogue Communication Systems:
3.8.1 Parseval's Theorem says that:
The total power in a power signal is its time ...
- 33
3
votes
1
answer
182
views
Proof of the Wiener-Khintchine theorem in time domain
In a proof for the Wiener-Khintchine theorem (See p. 572-573)
I have seen the following operation being done:
\begin{align*}
S_{xx}(f) &= \lim_{T \rightarrow \infty} \int_{-2T}^{2T} Rxx(\tau) e^{-...
- 95
-1
votes
1
answer
178
views
Autocorrelation of a random process
I have some doubt about the following exercise.
Let's consider the signal $X(t)= \operatorname{rect}\left(\frac{t}{2A}\right) $ , where $A$ is a
discrete random variable which can assume one value ...
- 75
0
votes
0
answers
48
views
Symmetric Autocorrelation Function vs Asymmetric Autocorrelation Function
I am trying to work through the Cyclostationary Blog to create a cyclic autocorrelation function:
I have been given the above equation to determine the cyclic autocorrelation function where tau is ...
- 33
2
votes
1
answer
310
views
Autocorrelation function of a filtered periodic signal
I'm having trouble with this exercise.
The signal $x(t)= \cos(2\pi f_0 t)$ is sent in input to a non-linear system with input-output relationship equal to: $g(x)= 0$ if $x<0$ and $g(x)=3x$ if $ x &...
- 75
0
votes
0
answers
29
views
Compute a waveform with given autocorrelation function
In the past few days I have been stuck with the problem of recreating the derivation shown in this paper, where they try to construct a waveform with a certain autocorrelation function.
Given a ...
0
votes
1
answer
197
views
Correlated phase noise
I am trying to find a mathematical model to understand the correlated phase noise.
Here, I see the reference phase noise is almost the same after up-conversion and then down-conversion. How does ...
9
votes
4
answers
1k
views
When is it true that "the Fourier transform of the autocorrelation is the spectral density"?
I am currently struggling on the book "System Identification: Theory for the User" by Lenart Ljung (freely available here) about the definition of the spectrum (around page 33). As I have ...
- 487
3
votes
0
answers
132
views
Emergence - what constitutes a minimally coherent source that "just begins" to produce stationary interference patterns?
A superposition of two signals with different frequencies will never produce visible (i.e. stationary) interference patterns. Such waveforms will produce spatiotemporal beat patterns, but they rapidly ...
- 131
1
vote
2
answers
63
views
how to find type of a binary sequence
I want to know how I can find the type (algorithm) of a binary sequence at hand.
For instance, I'd like to know whether the following (binary) sequence is m-sequence, Barker, Gold, etc.
AC DD A4 E2 F2 ...
- 95
0
votes
0
answers
24
views
Prefactor in autocorrelations?
I am new to the signal processing domain but wanted to ask what exactly is meant by prefactors here. A relevant resource/ solution would be helpful.
1
vote
1
answer
188
views
Continuous autocorrelation
Is there a known algorithm or an existing implementation that performs a "continuous autocorrelation"?
Meaning, in a situation where I sample a signal and every time I get a new sample (or ...
- 111
2
votes
1
answer
223
views
scipy convolve and fftconvolve return different output [closed]
I'm writing an autocorrelation function using and I noticed a difference between fftconvolve and convolve that should use fft if it's faster.
This is my function with convolve:
...
- 131
0
votes
0
answers
35
views
Reducing or removing autocorrelation in spatially correlated data
I am trying to figure out how one can reduce or preferably remove autocorrelation in spatially correlated data. Using the R code below, one generates spatially correlated data that is normally ...
- 1
-1
votes
1
answer
68
views
Expected value and autocorrelation
I have a wide sense stationary stochastic process ${{X_t;t\in \Re}}$ with mean 0 and autocorrelation function $R_x(\tau)=1-\frac{1}{4}|\tau|$ for $|\tau|=0,1,2,3;$ and zero anywhere else. I'm supposed ...
1
vote
1
answer
116
views
Find $E[Z^2(t)]$ when $Z(t) = X(t) - Y(t)$ where $Y$ is the output of a LTI system with WSS process $X$ as its input
I received this as a practice problem (part b only).
I was able to figure out that $E[Z^2(t)]$ = $R_X(0)+R_Y(0)-2R_\text{XY}(0)$ but did not see how to continue.
Checking the answers, I saw this line ...
- 113
2
votes
0
answers
144
views
Effect of down-sampling to PSD from auto-correlation?
I have a problem to evaluate the PSD from auto-correlation.
As you know, PSD is the Fourier Transform of the auto-correlation.
But I observe the spur at PSD when I calculate the auto-correlation with ...
- 21
0
votes
0
answers
119
views
What happens if you use the Fourier transform of the autocorrelation of a non-WSS process to compute power spectral density?
The Wiener–Khinchin theorem states that the power spectral density of a wide-sense stationary stochastic process can be obtained through the Fourier transform of the autocorrelation of the signal i.e.
...
- 173
7
votes
4
answers
779
views
Estimating period of low frequency oscillations: autocorrelation vs. Frequency approaches
I have a noisy signal around $15\text{s}$ long sampled a $32\,\text{Hz}$.
I am trying to estimate the peak frequency or period for a low frequency component with expected frequency in between $0.08\,\...
- 171
4
votes
3
answers
785
views
The normalization of the autocorrelation function and how it changes the definitions you've learned about signal analysis in communication systems
Since this question is book-oriented, I will kindly ask you to accompany it with a book that is considered by many researchers the bible of Digital Communication: Proakis - Digital Communications, one ...
- 337
1
vote
0
answers
58
views
How to analyse signal where one sample (timestamp) captures multiple data points
I have a process that captures interactions between a source and a sink. Unfortunately, the timestamp on the sample is one day. This means that regardless of the number of interactions (flows of ...
- 133
1
vote
2
answers
187
views
How does Power Spectrum remain symmetric in Z domain?
Can you tell me how the $P_x(z)=P_x^*(1/z^*)$ is mathematically correct. I can understand the $P_x(e^{jw})=P_x^*(e^{jw})$ as $P_x$ is real value. But why take the Z domain representation in this way ($...
1
vote
2
answers
169
views
Why is Autocorrelation between a Zero-mean Random process and a finite deterministic sequence zero?
The Solution is given above:
The Question is, how did the $\mathbb{E}{[x(k)f(l)]}$ and $\mathbb{E}{[x(l)f(k)]}$ become zero? is there some rule that correlation between Random Process and ...
1
vote
0
answers
27
views
How to show that the autocorrelation function of the given discrete function is this for autoregressive model(AR(2))?
This question is related to white noise representation of WSS sequences using AR(2) (autoregressive) model
The function is given as:
$$x(k)=\frac{1}{p_1-p_2}(p_1^{k+1}-p_2^{k+1})w[k]u[k]$$
where $w[k]$...
- 181
1
vote
1
answer
158
views
Autocorrelation of random walk
I want to analyze the auto-correlation of a received power signal that I captured. Unfortunately, I cannot publish the data but I found the same problem arises for a random walk, that's why I used the ...
- 13
2
votes
1
answer
327
views
The autocorrelation vector of frequency data
I am trying to find the correlation of audio frequency data resulting from an FFT with itself. It would be interesting to hear what you all think on the following question :
Should one use the complex ...
- 41
2
votes
1
answer
252
views
What is the Laplace Transform of the output power spectrum if the input signal is a white noise?
Let us consider a random wide-sense stationary process $n(t)$, which passes through a filter $h(t, \tau)$. Its autocorrelation function is
$$R_{n^\prime}(t)=\int_{-\infty}^{\infty} \int_{-\infty}^{\...
- 369
0
votes
2
answers
250
views
Extract a signal from noise, so I can view noise spectrum only?
I have a perfect modulated signal.
I have the same signal but with noise, this noise is from non linear amplification.
Is it possible, to extract the clean signal so it's just leaving the noise? The ...
- 43
0
votes
1
answer
339
views
Autocorrelation and the dot product of complex signals
I have a question for the signal processing community.
When trying to calculate the autocorrelation of an array containing complex data, could the result be purely imaginary, and is there any ...
- 41
3
votes
2
answers
268
views
Autocorrelation & Cross-Correlation -> Main uses in DSP??
Please help understanding the DSP usage of Autocorrelation & Cross-correlation
It seems this is strongly linked to calculating phase offsets, frequency offset for carrier recovery, symbol timing ...
- 97
4
votes
1
answer
496
views
Analysis of two audio signal by autocorrelation
I have recorded my audio by two hardware, PC and Microcontroller, I know the PC result are correct but my signal have some deficit. I have recorded by my PC and MCU my voice 6s 7812Hz and ...
- 363
-1
votes
1
answer
106
views
Deterministic process, what is it ? how can i get a better intuition for it?
so I was following this code where the author cleans the data for a time series problem. He does some feature engineering , all is well and good
until he does this
...
5
votes
1
answer
88
views
The Amplitude of the Correlation Function Peaks After Matched Filtering
I have 2 signals: $s_1(t)$ and $s_2(t)$. The autocorrelation functions are given by $R_{s_1}(\tau)$ and $R_{s_2}(\tau)$ with $|R_{s_2}(\tau)|<|R_{s_1}(\tau)|$.
I would like to know if the previous ...
- 51
0
votes
1
answer
286
views
How to draw the PSD from a time series
I try to draw the spectral density of a time series in order to compare it with the theoretical one.
Please can any one help me to do this.
This is the time series of all the data.
Thanks Dan Boschen ...
0
votes
1
answer
206
views
How to determine multiple Periodicities present in Timeseries data?
My objective is to detect all kinds of seasonalities and their time periods that are present in a timeseries waveform.
I'm currently using the following dataset:
https://www.kaggle.com/rakannimer/air-...
- 11
0
votes
2
answers
311
views
Power spectral density and auto correlation function: Frequency vs time representation
I have a time correlated periodic signal $a(t)$ with $t=0,1,...,T$ and $a(t+T) = a(t)$ that has been sampled at rate $\Delta t$ and I analyse the signal using the PSD via FFT and the ACF. As far as I ...
0
votes
1
answer
166
views
Is maximum cross-correlation achieved at the origin?
Let $x[n]$ and $y[n]$ be two DT random signals with $x[n]\xrightarrow{\mathcal{H}}y[n]$ through some system $\mathcal{H}$ that is deterministic yet unknown.\
Define both the autocorrelation and cross-...
- 129
1
vote
1
answer
143
views
Sampling rates for uncorrelated samples
I'm given the autocorrelation of a WSS random process
and the question asks to find the sampling rate that yields uncorrelated samples.
As far as I understand where looking for the $\tau$'s where $...
- 267