# Questions tagged [random-process]

A random process (in time), also called "stochastic process" is a signal that, when sampled at any given time, is a random variable.

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### Power Spectrum Density and Frequency

if i have some random signals (sampling rate = 10Hz, 0.1s per data) Using python library i transformed it to power spectral density power spectral density forms = f, psd (using mlab.psd) I'm really ...
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### Energy Detection in Presence of Colored Gaussian Noise

Before asking my question, let me introduce the context: For spectrum sensing based on energy detection, which has been widely studied in presence of AWGN, the optimal detection threshold is computed ...
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### Calculation of an autocorrelation function

A sample of a random process is given as: $$x(t) = A\cos(2\pi f_0t) + Bw(t)$$ where $w(t)$ is a white noise process with $0$ mean and a power spectral density of $\frac{N_0}{2}$, and $f_0$, $A$ ...
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### Random telegraphic noise and Lorentzian noise power spectral density

Following the example of the Lorentzian noise power spectral density shown above (ref), I would like to clarify the following: In the first figure (labeled by (c)), May I please know why the constant ...
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1 vote
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### Incorrect Power Calculation in MATLAB Convolution

I have been working on a MATLAB code to perform convolution and calculate the power of the resulting signal. However, I have encountered an issue with the power calculation in my code. I am convolving ...
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1 vote
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### Does bandlimited power spectral density correspond to original WSS random process being bandlimited almost surely?

If it is given that PSD of a random process is bandlimited to frequency $f_B$, then can we claim that any sample path of the random process is also bandlimited to $f_B$? Intuitively, I always thought ...
1 vote
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### Power Spectral Density and Wiener–Khinchin theorem for 2 different stochastic processes

I know the famous Wiener-Khinchin theorem for stationary random processes: the Fourier transform of the autocorrelation function of a stationary random process is equal to the Power Spectral Density ...
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1 vote
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### Why different noise terms are read at specific sampling interval in Allan Variance plot?

I was trying to identify Quantization Noise, Angle Random Walk, Bias Instability, and Rate Random Walk from Allan Variance plot which as Allan deviation on y axis and Sampling Time Interval ...
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### Struggling with visualizing (drawing) a sample of a random process

I've had this question I don't really know how to answer. let $t \ge 0$, $N_t$ is a possionian random process with parameter 1. let $-\infty < t < \infty$, $X_t$ is a random process that is ...
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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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### The frequency function for $Y_t-18=0.4X_t+0.9X_{t-1}+e_t$

I am having trouble finding the frequency function that takes me from $X_t$ to $Y_t$ in the system stated in the title. $X_t$ and $Y_t$ are stationary stochastic processes and $e_t$ is zero mean white ...
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### What is the difference between Yule Walker and Modified Yule Walker Equation that used in Stochastic Signal Modeling?

Our Professor couldn't explain the clear difference between the Yule Walker equation and the Modified version of it that is used in Stochastic models. Please explain both the equations and why we ...
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### Probability of the rate of change of a filtered random process

I am given the following problem: I have a filter with impulse response $h(t) = e^{-10t}, t \leq 0$, and autocorrelation function of the input signal, which is WDS and Gaussian with median equal to 0, ...
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### The definition of amplitude probability density

I'm trying to figure out the formal definition of "amplitude probability density"(APD). First of all I didn't find a textbook which defines APD but there are some sources that explain it ...
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### Global variability index for group of signals

Suppose I have a method that I can use to generate $n_p$ signals (we can intend them as realizations of an unknown not stationary discrete-time stochastic process). Modifying the method, I can obtain ...
200 views

### Signal-to-Noise ratio of multivariate stochastic process from Correlation Matrix

I'm not in signal processing, I'm from an another discipline. I've derived a simple result which I presume must be well known in SP and I'd like to know whether there's a paper or textbook that has it ...
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### How to characterize the randomness of an event using it's PSD?

I have the power spectral density function of a stochastic phenomenon. how can I generate a signal (time series) representing the randomness of this event over time? How can I draw the probability ...
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### How to compute the energy of a NON-STATIONARY (transient) random discrete-time signal

When computing the energy of a NON-STATIONARY (transient) random discrete-time signal $x(n)$, does it make more sense to compute the energy as $E=\sum_1^N{x^2(n)}$ over all the $N$ samples or does ...
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### Proof of weak stationary random process autocovariance always goes to zero?

Professor told me that if a random process is weak stationary, and it does not feature any periodic component, then its autocovariance always goes to zero. I can intuitively understand it, however, ...
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### Is the expectation of a random process $X(t)$ with zero DC component necessarily zero?
Is the expectation of a random process $X(t)$ with zero DC component necessarily zero? Or can it be non-zero depending upon the process?