# Questions tagged [autocorrelation]

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

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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 ...
1 vote
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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 ...
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 vote
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### 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 ...
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 ...
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 ...
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 ...
1 vote
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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 ...
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
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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 ...
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: ...
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### 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 ...
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
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### 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 ...
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### 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 ...
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. ...
779 views

1 vote
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### 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
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### 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 $w[k]$...
1 vote
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 ...
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 ...
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}^{\...
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 ...
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 ...
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 ...
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 ...
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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 ...
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 ...
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-...
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 ...
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-...
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 \$...