# Questions tagged [random-process]

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### Moving from deterministic signals to stochastic signals in s-domain (Power Spectral Density)

Assume we have the following system (coming from control systems theory, hence in s-domain) $Y(s) = H_A (s) \cdot A(s) - H_B (s) \cdot B(s)$ I now wish to consider $a(t)$ and $b(t)$ as white noise ...
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### moving average rounding error analysis

I have implemented a moving average, similar to the Hogenauer Filter, with a reduced number of computation operations. I expect the expected error to behave as the random walk and its STD to be of ...
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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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### Proving the upper bound of cross correlation

I am reading about cross-correlation from this document and equation (5) states that The maximum value of the crosscorrelation is not always when the shift equals zero; however, we can prove the ...
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### Signifance of statistical information in a signal

I am learning control engineering for some time and I work with a lot of transfer functions and frequency domain design. Reading from textbook, to me everything seems deterministic. Whenever I come ...
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### Conceptual Questions on Colored Noise Process

I am having a tough time finding answers to some specific questions and finding references where there is information regarding Brownian noise or Red Noise. I'm referring to white and colored noises ...
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### Is white noise WSS by nature or not?

I want to know what is the difference between white noise and WSS white noise. is there any difference between them or they're equal? and what about white Gaussian Noise?
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### Practical implementation of Expected Value?

If i compute the average power of my input signal random variable $X(t)$ as $$R = E[X^2(t)]$$ i.e. as the expected value of a random process, is this really just an estimate of average power? More ...
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### Why the requirement of the GCD of the lengths of all circuits in the graph being one?

I am reading A Mathematical Theory of Communication. The second requirement of an ergodic process confuses me (emphasis mine): All the examples of artificial languages given above are ergodic. This ...
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### Cyclostationary signal intuition

Images show a discussion I picked up from a PhD thesis about a cyclostationary process and need help interpreting it. "In the time domain the upsampling process creates a signal whose distribution of ...
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### How to create a wide-sense stationary time series with a frequency of 40 Hz?

I want to create a time series in MATLAB which has a peak frequency of 40 Hz but is also a wide-sense stationary random process. I then want to use power spectral density estimation to recover the ...
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### question related to something in karlin and taylor stochastic processes one text

This question is essentially a question about something in Karlin and Taylor's Stochastic Processes One text in the spectral chapter. Since this is a DSP list, Karlin and Taylor may not be so popular ...
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### Example of Entropy and Channel Capacity Computation

Can you help me on verifying if this computation of entropy is correct and on understanding its meaning? I am not sure of the result especially because it is equal to 0: it means that we cannot ...
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### Randomly Generate Synthetic Noise in an Image Text Document

I'm working on denoising dirty image document. I want to create a dataset wherein synthetic noise will be added to simulate real-world, messy artifacts. Simulated dirt may include coffee stains, faded ...
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I have a wide-sense-stationary (WSS) process $\{x(t)\}$ and two linear filters with impulse functions $h_1$ and $h_2$. Let $\delta(\omega)$ be the power spectrum of $\{x(t)\}$ and $$H_1:\omega\... 1answer 590 views ### PSD from autocorrelation in MATLAB I am trying to simulate a simple stochastic process defined by the equation: \begin{equation} \frac{1}{v}\frac{db}{dt} +\Gamma_0 b= \sqrt{\sigma}R(t), \end{equation} where R(t) is a zero-mean white ... 2answers 131 views ### Why is there only one integration in the solution if there is two integral in the formula? In this problem the random variable is theta and according to the formula there should be two integrations but in the solution there is only one . Nor am i able to understand the meaning of x1 and x2 ... 0answers 63 views ### 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, ... 1answer 74 views ### Question regarding AC power of ergodic process We know Ergodic process is the subset of Weakly stationary process which permits us to substitute time average for ensemble Average My teacher said If X(t) is Ergodic random process then following ... 1answer 152 views ### Correlation of independent random processes Suppose X(t) and Y(t) be two independent random processes. Is E(X(t_1)Y(t_2)) necessarily zero? 1answer 451 views ### Power contained in a random process X(t) How do we calculate the AC and DC power of random process X(t) , provided we have R_x (\tau), and S_x(f) ? 0answers 31 views ### 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? 1answer 78 views ### Variance of function of random variable Is their an easier way to find variance of function of random variable? Till now what I am doing is first find probability density function of (function of random variable) then integrate over range. 2answers 52 views ### Independence of Functions of random Variable Consider I am given two functions of one random variable each for example x=cos(at),y=rect(bt) where a and b are random variables.And I am given Probability density function for a and b then if I am ... 4answers 113 views ### What is definition of independent random variable I wan't to ask that if E{X}=0 E{Y}=0 and E{XY}=0 then how can I verify if the two random variables are independent or not. X , Y are both continuous random variables {I am not able to recall ... 2answers 64 views ### Intuition about independent signals Given is this Wiener filter: From this we take \begin{equation} x[k]-a x[k-1]=v[k] \end{equation} v(k) is assumed to be a white gaussian noise. In the textbook it is then stated that The ... 0answers 18 views ### Early estimate the sign of the drift in a generalized Wiener process I posting here my problem, perhaps somebody can point me how to proceed further :) [The challenge] I have an electronic system that can be modeled as a Wiener process with a drift \mu:  X_t = \... 1answer 102 views ### Power Spectrum Estimation of three sinusoids in white noise Let's assume we have a random process consisting of three sinusoids in white noise:$$x[n] = 3 \cdot \sin(ω_1 \cdot n + ϕ_1) + 5 \cdot \cos(ω_2 \cdot n + ϕ_2) + 2 \cdot \sin(ω_3 \cdot n + ϕ_3) + v[n]$$... 1answer 89 views ### An Interesting Model with Unknown Orthogonal Design Matrix Suppose the multivariate one-way anova model for the raw data , i.e.$$ \label{Example_model_1} \mathbf{y}_{ij}=\mathbf{\mu}+\mathbf{z}_i+\mathbf{e}_{ij}, ~~ i=1,\ldots,m,~~j=1,\ldots,n_i,~~~~~~~~~~...
The root mean square $$\sigma_{x} = \sqrt{\frac{1}{T}\int_0^T x^2(t) \, \mathrm{d}t}$$ of a finite zero-mean random signal $x(t)$ in the range $0 < t < T$ is related to the signal's power ...
I have a sequence such as $$r[n] = y[n]v[n]$$ $y[n]$ and $v[n]$ are zero-mean and statistically independent. I need to find a variance of $r[n]$ and show that it is white and equal to \$\sigma ^2_y\...