# Questions tagged [random-process]

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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 ...
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### Random Signal Energy

Why the energy of random signal(random process) is infinite? and why random signal can not be zero at infinity? I know that there is a relation between the tow questions but I'am still confused.
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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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168 views

### Generating violet noise with a specific PSD coefficient

I am trying to generate a time-domain violet noise signal with the following power spectral density (PSD): $$S_n(f) = A^2f^2$$ Unfortunately, I am having trouble finding the right amplitude ...
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1 vote
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### How to generate a power-law / pink noise signal?

Suppose I need to generate a time series where the intervals will be about 120 seconds every time, but with a small variation (e.g. 125, 130, 119, 118, 121, 129, etc) I want this variation not to be ...
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### Is "Introduction to Statistical Signal Processing" by RM Gray good for starting?

I am working on noise processes in electronic devices for my studies, by now Ive been doing a fairly large amount of processing of time measurements, like calculate PSD, estimate thermal, flicker ...
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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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### related to random nature of wireless channel

I am reading An Approximate BER Analysis for Ambient Backscatter Communication Systems With Tag Selection wherein it is mentioned that "when the distance between two nodes is very small and line ...
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### Frequency response terminology: $N(i\omega)$, $Q(i\omega)$

I am reading through an analysis of a system $$Y(t) = \frac{d}{dt}X(t) + X(t)$$ and the frequency response $H(i\omega)$ is defined as  H(i\omega) = \frac{N(i\omega)}{Q(i\omega)} = \frac{1+i\omega}{...
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1 vote
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### How to Combine white gaussian random noises from different Seeds?

I have generated two different white gaussian random noises in MATLAB using two different seeds. For example: ...
1 vote
103 views

### What's a Normalized function?

I'm studing Representations of Random Processes and the book talks about Orthonormal functions, but doesn't make it clear what is it. I was able to realize that a set of functions are orthonormal if ...
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### RMS Amplitudes of voltage

I am looking here at the course of current fluctuations and have calculated the RMS values, but somehow it seems strange to me: with the black line there are small fluctuations, but the RMS value is ...
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1 vote
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### Why is Power spectral density of random walk noise defined despite it being non-stationary? [duplicate]

While reading up on oscillator stability, I noticed that authors characterize random walk noise (Brownian noise) as having a PSD of $S_y(f) = h_{-2} f^{-2}$ where $h_{-2}$ is some constant. This is ...
1 vote
96 views

### 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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### 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 ...
119 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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1 vote
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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 $Y(t)$ ...
46 views

### 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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1 vote
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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 ...
193 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 ...
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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 ... 445 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 ...
52 views

### 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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1 vote