# Questions tagged [random-process]

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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 ...
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### 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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### Response of an unstable LTI system to random signals

A convenient approach for studying the response of a stable LTI system with impulse response $h(t)$ to a WSS stochastic input $X(t)$ is to look at the power spectral density (PSD) of the output $Y(t)$ ...
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### mathematical expression to detect modulated data within a vector

Assume I have such modulated data which is, for example, $x=0.7+0.7i$. That modulated data is encapsulated in a vector as below: OR where $c$ is any constant number, let’s say, for example: $c=0.7$ ...
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### Under what conditions is there a one-to-one mapping between continuous-time and discrete-time signals?

As the sampling theorem dictates that the uniform sampling frequency must be at least twice the maximum frequency present in the bandlimited signal (Nyquist rate), a question arises about the ...
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### Variance of filtered white noise

I was asked a question, as posted here, and the answer given is (A) i.e. $\frac{3}{2} A^2 N_0$. My solution steps was: Finding the mean of the output process: Since input is gaussian the output will ...
87 views

### Variance of Integral of a real white Gaussian Noise Process

In this question, is the answer not equal to infinity ? Answer is mentioned as 6. But my doubt is cant we think of it like a linear combination of many independent random variables each having ...
57 views

### 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 ...
136 views

### 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 ...
129 views

### 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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### Cross-correlation of filtered random processes

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\...
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### PSD from autocorrelation in MATLAB

I am trying to simulate a simple stochastic process defined by the equation: $$\frac{1}{v}\frac{db}{dt} +\Gamma_0 b= \sqrt{\sigma}R(t),$$ where $R(t)$ is a zero-mean white ...