Skip to main content

Questions tagged [autocorrelation]

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

Filter by
Sorted by
Tagged with
0 votes
1 answer
34 views

Autocorrelating output signal which sampled at rates higher than signalling rate

A bpsk signal(a$_{n}$) with d$_{min}$ = 1, passes through a pulse shaping filter p(t), the resultant pulse shaped signal ($\sum_{n=0}^{k-1} a_{n}p(t-nT_{s})$) passes through an AWGN channel which adds ...
DarkKnight_007's user avatar
0 votes
0 answers
24 views

Identification of the spectrum color of a coded video signal

I have two encoded video signals (MPEG and H.263). In each file, I have information about the frames of the video. I calculated the autocorrelation and then did the Fourier transform to find and plot ...
user72361's user avatar
2 votes
1 answer
78 views

How should I go about completely decorrelating a digital signal?

So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
2 False's user avatar
  • 45
0 votes
3 answers
116 views

Rigorous derivation of autocorrelation of white noise

It is said that the autocorrelation of white noise is the dirac delta function $\delta(\tau)$, but I don't know how to derive that... Since white noise is a function with constant power spectral ...
Mashe Burnedead's user avatar
1 vote
0 answers
72 views

How to calculate the cross-correlation of two signals that have different sizes?

I have two video signals of the same video. One encoded in MPEG format and the other in H.263 format. These signals are represented in .txt files with the frame sizes in an array. I need to calculate ...
user72361's user avatar
0 votes
2 answers
63 views

Can Autocorrelation be used to Differentiate Signal Quality (High, Medium, Low, Very Low) for Periodic Signals?

I'm working on a project to classify the quality of periodic signals into four categories: high, medium, low, and very low (noisy). I was initially exploring autocorrelation as a potential feature for ...
Mamad Fasih's user avatar
0 votes
1 answer
88 views

Significance of imaginary part of auto-/cross-correlation

In this answer to this question, we get a hint that there is a significance to the imaginary part of the auto-correlation function, and that we should try to calculate the correlation with the real ...
Andréas Sundström's user avatar
0 votes
2 answers
42 views

Unbalanced binary sequences for system identification?

I have a physical system that I'd like to obtain the frequency response for. I can only provide binary sequences as inputs to the system. Normally, I'd use a MLS (maximal length sequence) and ...
tkw954's user avatar
  • 203
0 votes
1 answer
118 views

Cross Correlation Peak Value of Wideband signals - The Phase and Sample Offset are related but how

Two CDMA Codes or Gold Codes or PRN Sequencies, i.e. a pattern in time, are cross correlated in the time domain. However one of them is delayed compared to the other. How is the phase argument of the ...
njk7's user avatar
  • 45
0 votes
0 answers
11 views

Difference transformation and Stationarization of Moving Average

I have a temperature sensor data, I want to denoise it. The first thing that came to my mind was to take the moving average, it was very smooth but it is still not stationary. If I take the log ...
Clankk's user avatar
  • 1
1 vote
1 answer
106 views

Blackman-Tukey PSD in Python

I am trying to calculate the Blackman-Tuckey (BT) PSD in Python to check my understanding (getting started with signal processing). I have tried making the calculation myself and compare it with Scipy'...
opengisapprendice's user avatar
3 votes
1 answer
97 views

Does oversampling lead to colored noise?

Suppose we receive $R(t)=X(t)+W(t)$, where $X(t)$ is band-limited to $[-B/2, B/2]$ and $W(t)$ is white Gaussian noise with autocorrelation $R_W(\tau)=\frac{N_0}2\delta(\tau)$. If we filter $R(t)$ ...
syeh_106's user avatar
  • 223
2 votes
1 answer
88 views

Cross-correlation between brain signals: how to handle autocorrelation?

I've been asked to calculate the cross correlation in the 3-12 Hz band between two simultaneously recorded brain signals in two distinct brain areas. Data were acquired at 32 kHz then preprocessed by ...
NeuroDSP's user avatar
0 votes
0 answers
48 views

i am stuck on question 3 and isn't getting desired output. can anyone explain what should i do and provide code for this?

Given the autocorrelation function ACF(n)=cos((2/30)n) for n= -5,-4,…0,1,…, 5 use the simplified Lim & Malik iterative algorithm to extend the ACF to 256 points. Note that the simplified version ...
Thouhidul Islam's user avatar
1 vote
1 answer
127 views

Interpretation of a non-canonical Allan Variance plot

I am currently working on characterizing the noise sources of a Global Navigation Satellite System (GNSS) sensor using an Allan Variance plot, which is commonly employed to analyze frequency stability ...
RoninAmibo's user avatar
2 votes
2 answers
312 views

How to find the pattern of a signal or main cycle of a signal?

I have a dataset where a certain pattern is repeatating in different time interval. The repetation of data pattern can come with slight change. I want first find the pattern (or cycle) and later by ...
asteroid's user avatar
0 votes
0 answers
67 views

Signal Correlation time computation for Time delay estimation

I need to compute the Signal Correlation Time of an audio signal to check wether time-delay estimations are anomalous. In paper The Signal correlation time is defined as the width of the main lobe of ...
Luca's user avatar
  • 108
1 vote
1 answer
86 views

$i^{\text{th}}$-dimensional autocorrelation function

I am referring to the work of Stephen A. Billings on "Identification of a class of nonlinear systems using correlation analysis" from the year 1978, where it is mentioned that the $i^{\text{...
Neuling's user avatar
  • 103
0 votes
2 answers
72 views

Fundamental question about Autocorrelation

I need help! I'm trying to calculate the Power Spectral Density of a quantum operator ($\delta \hat{n}(t)$) given by: $$ \delta \hat{n}(t) = A(t)\delta\hat{a}(t)+A^{*}(t)\delta\hat{a}^{\dagger}(t) $$ ...
Pedro Pinho's user avatar
1 vote
1 answer
81 views

Zero-mean preprocessing before calculating the autocorrelation

I am aware that if we do not subtract the mean value from the white noise at the beginning (if the mean is not equal to 0), that its autocorrelation function will be triangle shaped and not a delta ...
vakula85's user avatar
0 votes
1 answer
160 views

Calculation of frequency correlation function based on power delay profile

We know that the frequency-domain correlation function and the power delay profile appears as a Fourier transform pair, i.e., $$A_{c}(\Delta f) = \int_{-\infty}^{\infty}PDP(\tau) \cdot e^{-j2\pi \...
Vic's user avatar
  • 113
1 vote
0 answers
43 views

Calculation of the discrete cosine transform

I am wanting to use the discrete cosine transform to relate the autocovariance function of a process to its periodogram. Following Chris Chatfield's book (Time Series Analysis, p129), I am wanting to ...
hydrologist's user avatar
1 vote
1 answer
77 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 ...
Javad Ibrahimli's user avatar
1 vote
1 answer
82 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 ...
scc28adi's user avatar
1 vote
1 answer
48 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] ...
Mark Boccelli's user avatar
3 votes
1 answer
254 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 ...
Xiangyu Cui's user avatar
1 vote
0 answers
57 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...
Thabile 's user avatar
1 vote
1 answer
279 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 ...
requiemman's user avatar
1 vote
1 answer
81 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 ...
chinmayeelm's user avatar
0 votes
0 answers
23 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 ...
CfourPiO's user avatar
  • 107
1 vote
0 answers
78 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; ...
EricH's user avatar
  • 11
1 vote
1 answer
120 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 ...
DataPhysicist's user avatar
0 votes
1 answer
221 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?
anni_m's user avatar
  • 1
2 votes
1 answer
561 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 ...
SS1's user avatar
  • 33
3 votes
1 answer
374 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^{-...
Finn Heijink's user avatar
-1 votes
1 answer
234 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 ...
Maghreb_1911's user avatar
0 votes
0 answers
76 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 ...
SS1's user avatar
  • 33
3 votes
1 answer
381 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 &...
Maghreb_1911's user avatar
0 votes
1 answer
334 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 ...
Krishna K Gurumoorthy's user avatar
10 votes
4 answers
2k 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 ...
NokiYola's user avatar
  • 507
3 votes
0 answers
133 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 ...
srhslvmn's user avatar
  • 131
1 vote
2 answers
87 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 ...
Ali's user avatar
  • 95
1 vote
1 answer
282 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 ...
Arik Yavilevich's user avatar
2 votes
1 answer
299 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: ...
Adam Katav's user avatar
0 votes
0 answers
55 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 ...
Show's user avatar
  • 1
-1 votes
1 answer
86 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 ...
A couple of three things's user avatar
1 vote
1 answer
156 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 ...
Robert Moore's user avatar
2 votes
0 answers
159 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 ...
David's user avatar
  • 21
0 votes
0 answers
154 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. ...
Tommy Wolfheart's user avatar
8 votes
4 answers
918 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\,\...
00__00__00's user avatar

1
2 3 4 5
10