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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Autoccorelation of a Random Process with Rectangular Pulses
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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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'...
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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 $R(t)$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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$i^{\text{th}}$-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 $i^{\text{...
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Fundamental question about Autocorrelation
I need help!
I'm trying to calculate the Power Spectral Density of a quantum operator ($\delta \hat{n}(t)$) given by:
$$ \delta \hat{n}(t) = A(t)\delta\hat{a}(t)+A^{*}(t)\delta\hat{a}^{\dagger}(t) $$
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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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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.,
$$A_{c}(\Delta f) = \int_{-\infty}^{\infty}PDP(\tau) \cdot e^{-j2\pi \...
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Calculation of the discrete cosine transform
I am wanting to use the discrete cosine transform to relate the autocovariance function of a process to its periodogram. Following Chris Chatfield's book (Time Series Analysis, p129), I am wanting to ...
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Power Spectral Density and Total Power Calculation for Signal
I am currently working on analyzing a signal with the autocorrelation function given by:
$$R(\tau) = 100 \cos( 10000\pi\tau) (Λ(2000\tau))^2$$
I need assistance in plotting the power spectral density ...
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Frequency content of a noisy signal
To find the frequency content of a noisy signal (PSD), there are two methods below:
#1 Take the fourier transform of its power signal (square the noisy signal)
#2 Find the autocorrelation function of ...
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Finding mean, autocorrelation, and power spectrum of $y[n]=(x∗h)[n]$ where $x[n]$ is zero mean white gaussian noise
If given $x[n]$ is zero mean white Gaussian noise with variance $\sigma_x^2$, and a filter with a known impulse response $h[n]$, how would I find the mean, autocorrelation, and power spectrum of $y[n] ...
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What's the exact definition of the power spectral density function?
I learned from my signal processing course that PSD is the Fourier transform of the autocorrelation function.
$$\mathscr{F}\Big\{\mathrm{E}\big[x(t)x(t+\tau)\big]\Big\}$$
Today I took my statistic ...
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Autocorrelation-properties
How do we go about proving the property that entails; If X(t) is ergodic with no periodic components the autocorrelation converges to square of the mean as the time difference(τ) approaches infinity
𝝁...
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Proving that the autocorrelation of a signal is the convolution with its time-reversed complex conjugate
I need to prove the property $$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 ...
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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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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 ...
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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 ...
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