Questions tagged [autocorrelation]

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

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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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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-...
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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 $...
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SNR calculation via autocorrelation

I am given the following task, however, I am lost conceptually, and require some assistance on the procedure. Given raw noisy data where the signal is a single sinusoid and noise is a random content. ...
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Hard time figuring out whether the following random process is wide sense stationary

I'm dealing with a random process that's simply a square wave with pulse period T, where: Each pulse takes either $A$ or $-A$ depending on a coin toss. The wave is shifted by a random $t_d$ where $...
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How design a filter to obtain a desired autocorrelation in output

I have a signal x(n) with a given autocorrelation function ACF, $R_x(\tau) \neq 0$ for $\tau=1, \cdots ,L$ My question is how can i design a filter (better with a few coefficients) to obtain a signal $...
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Fourier transform from the PSD

I need to compute the Fourier transform o the time derivative of the autocorrelation function (ACF) of a discrete signal with sign changed. Lets call it $Y(\omega)$. I had some computations problems ...
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Limiting value of autocorrelation of wide-sense stationary process

Let random process $X$ is wide-sense stationary process. Where could I find the source or verification of the statement that, when the limiting value of autocorrelation $\lim_{\tau\rightarrow\infty}...
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Is there relationship between autocorrelations Rx(2) and Rx(1)?

There is a random process, $X:\mathbb{Z}\rightarrow\mathbb{R}$ in discrete-time domain, which is wide-sense stationary with zero mean and autocorrelation function $R_X(\tau)$. a) What range of values ...
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Near Real Time Algorithm For Approximating Fundamental Frequency

I'd like to analyse the notes being played on a cello C2(65.4Hz) to C6(1046.5Hz) recorded on a PC and thus a likely sampling rate of 44.1kHz. If I can get that to behave then I'd like to be able to ...
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Specify a random process such that $R_Y[0]=3+u$, $R_Y[1]=-2+u$, and $R_Y[k]=u$ otherwise

there is a problem that I should specify a real-valued random process $Y[n]$ such that the autocorrelation function $R_Y[k]$ satisfies $$R_Y[0]=3+u,\ R_Y[1]=R_Y[-1]=-2+u,\ \text{and}\ R_Y[k]=u, |k|>...
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Frequency representation of relaxation processes

I simulated a discrete sample of a variable whose autocorrelation function (ACF) should theoretically be composed of a sum of exponential-like functions. My goal is to represent it in the frequency ...
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Confusion In DC power,Average Power,Ac Power and total Power

These are Things I studied. $ E[X]:-$ THis gives us Average value or Dc value $E[X^2]:-$Total power $\sigma^2=E[X^2]-E[X]^2$:-Ac power From Autocorrelation $R_x(0)=E[X^2]$--Total power And $ \lim_{x\...
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Autocorrelation via real FFT and real IFFT

I am working on a fast autocorrelation function using the FFT (similar to scipy.signal.fftconvolve). The algorithm is pretty straight forward but I feel like I'm ...
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dimensions of the autocorrelation function of white noise

My question concerns the dimensions of the autocorrelation function of the white noise. First is a short summary of what I understand about the random signals. If we have a stationary random signal $x(...
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Given an AR signal, find its PSD, its autocorrelation function

I am studying discrete-random signal processing, Could anyone tell me by an example or reference what it means by the following? Given an AR signal, find its PSD (power spectral density), its ...
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What is the meaning of WSS [duplicate]

I’m wondering what it means for a signal to be wss. I know that the statistics of a wss signal does not change over time because it’s mean is time - invariant, but what it means for the ...
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How to interpret values of the autocorrelation sequence?

I know that (auto)correlation indicates the "degree of predictability" of a variable with respect of another. However, this is a vague notion. I know that a blank process should have an ...
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Find some signal x[n] whose auto-correlation function is R[k] [closed]

I want to write a MATLAB code for generating a random message signal 𝑥[n] where its autocorrelation function is: R[k] = sinc^2 [1/4 k] where k is an integer. (Hint: Generate a process where ...
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How does the PSD depend on sample size?

My question is this: Do the 'amplitudes' of a PSD depend on the number of samples on which it is based? One definition of the PSD I have found is: $$ P_{xx}(\Omega_m) = \frac{X(\Omega_m)\cdot\bar{X}(\...
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Difference between reference and measurement signal?

Which differences can we find on various signals? We assume that we have a reference signal (determined theoretically) and measured signal. Which methods exist for determining the similarities ...
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Identify and remove repeated audio chunks

I have some audio produced by a buggy recorder, at some point it may start two recording streams, each stream captures chunks of audio and write to a file. The buffer queue is processed asynchronously,...
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2D space and 1D time evolution of a random field

I also asked this on math stack-exchange, but it is also relevant for the signal processing community. I want to develop a 2D random field and its change with time with constant velocity. My process: ...
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How to properly band-pass filter an autocorrelated signal?

Let's consider an example ECG time series, sampled at 360Hz: I verified that autocorrelating a signal preserves its frequency content. For instance, both original and autocorrelated data show the ...
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Auto/cross correlation for data set with multiple realizations

Context For an assignment, I need to find the correlation matrix of a dataset with 100 random variables and 1000 realizations for each. (It's a stock market example). Problem I don't understand how ...
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Kay Statistical Signal Processing Estimation Theory Example 7.14

Example 7.14 from Kay Estimation Theory A common WSS random process has the ACF $$r_{xx}[k]= \begin{cases} 1+b[1]^{2}+b[2]^{2} & \text{k = 0}\\ b[1] +b[1]b[2] & \text{k=1}\\ ...
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Noise model as Sinc function

In "Fundamentals of signal processing: estimation theory", example 3.13 Kay has used a model of band-limited Gaussian noise with a uniform PSD and a sinc autocorrelation function. I expected ...
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Beep Signal for Latency Calculation

I want to play audios on two mobiles with sync. But mobile phones are not in sync. I am trying to find two Mobile phones playing latency so I can pad latency on each phone so they can play together. ...
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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 ...
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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 \...
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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 ...
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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: ...
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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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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 (...
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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 ...
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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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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 ...
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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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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?
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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)^{...
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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 ...
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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 ...
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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 ...
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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 ...
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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}^{\...
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3 answers
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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) ...
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