Questions tagged [autocorrelation]

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

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Recreating the results shown in the following Figure: Textbook: DIGITAL SIGNAL PROCESSING IN MODERN COMMUNICATION SYSTEMS 2ed

I wrote the following code in MATLAB (the compared sequences are B[n] and C[n] provided in the code): ...
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Mistake in Python implementation of Pisarenko's harmonic decomposition

I'm trying to implement Pisarenko's Harmonic decomposition in Python and can't get a proper pseudo spectrum revealing the three frequencies of the signal I'm analysing. I tried a few things (using <...
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I’m working on the same exercise on this link and would like to modify the data related to the sequences $\mathcal B_k$. Specifically, I’m considering changing the probabilities or values of $\mathcal ... 1 vote 1 answer 86 views Impact of Time Shift$(\tau)$on Autocorrelation for a Rectangular Pulse Train Process I've been studying the autocorrelation function of a rectangular pulse train process, and I came across an interesting situation on this site link here where a time shift$\tau$was introduced. In the ... 2 votes 1 answer 69 views Relation and differences between correlation sequence and correlation matrix Suddenly I am stuck at a question while studying Statistical signal processing: What are the differences between correlation sequence and matrix (can be auto/cross), and how are the two related? When ... 0 votes 0 answers 38 views Time domain expression of a stationary continous broadband signal and its autocorrelation I want to find the auto-correlation of a stationary continous broadband signal. The auto-correaltion is $$f\star f=\int_{-\infty}^\infty f^*(t)f(t+\tau)\ \mathrm{d}t.\tag{*}\label{*}$$ The power ... 1 vote 1 answer 108 views Show that the impulse response of an LTI system can be determined by observing the output and inputting white noise Problem Show that the impulse response of an LTI system can be determined by observing the output and inputting white noise. Attempt Let$x(t)$be the input signal (white noise) and$y(t)$be the ... • 480 0 votes 1 answer 50 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 ... 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 ... 2 votes 1 answer 92 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 ... • 47 0 votes 3 answers 144 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 ... 1 vote 0 answers 89 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 ... 0 votes 2 answers 71 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 ... 0 votes 1 answer 120 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 ... 0 votes 2 answers 48 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 ... • 203 0 votes 1 answer 140 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 ... • 45 0 votes 0 answers 12 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 ... 1 vote 1 answer 153 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'... 3 votes 1 answer 108 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$R(t)$... • 223 2 votes 1 answer 96 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 ... • 21 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 ... 1 vote 1 answer 137 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 ... 2 votes 2 answers 512 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 ... • 21 0 votes 0 answers 69 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 ... • 108 1 vote 1 answer 87 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$i^{\text{...
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I need help! I'm trying to calculate the Power Spectral Density of a quantum operator ($\delta \hat{n}(t)$) given by: $$\delta \hat{n}(t) = A(t)\delta\hat{a}(t)+A^{*}(t)\delta\hat{a}^{\dagger}(t)$$ ...
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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 ...
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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 ...
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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 ...
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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; ...
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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 ...
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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?
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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 ...
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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^{-...
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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 ...
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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 ...
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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 &...
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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 ...
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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 ...
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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 ...
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