Questions tagged [random-process]

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24 views

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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1answer
115 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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1answer
85 views

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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1answer
42 views

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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42 views

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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1answer
46 views

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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2answers
37 views

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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1answer
36 views

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: ...
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2answers
63 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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1answer
31 views

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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47 views

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 ...
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1answer
58 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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34 views

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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59 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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34 views

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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1answer
43 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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3answers
163 views

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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1answer
29 views

Transformation of random variables vs shift of functions

I am a beginner to random variables and I am understanding the concept of the transformations of a random variable. Consider a random variable $X$ to be Gaussian distributed with $a_x = 1.6$ and $\...
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2answers
51 views

Intuitive definition of ergodicity for random signal

Is it possible to define the ergodicity of the random signal in an intuitive sense without using any statistical reference?
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3answers
74 views

voltage current analysis in time

I am looking at the transmembrane voltage of a neuron model and would like to investigate this in more detail. The applied current is divided into a deterministic and a noisy component - if I set the ...
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3answers
52 views

Signal variance and power connection

For a random signal $x(n)$, why is $E(x(n)^2)$ called signal power? Is it really power? Any proof?
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1answer
61 views

How to describe voltage fluctuations

I am looking for a way to describe the properties of voltage fluctuations - is the RMS amplitude a suitable measure? Attached is a screenshot showing the random current fluctuations (in the case of ...
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1answer
93 views

What is the relation between input and output PSDs given system transfer function $H(s)$

If I have the system transfer function $H(s)$ in the complex frequency domain, how would I relate the input/output power spectral densities? I have come across the relation $P_{out}(f) = |H(f)|^2P_{in}...
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1answer
64 views

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 ...
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1answer
129 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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2answers
69 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 ...
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1answer
284 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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49 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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1answer
229 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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0answers
27 views

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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1answer
90 views

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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3answers
610 views

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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1answer
137 views

Wide sense stationary that is not strict sense stationary? [duplicate]

A "wide-sense stationary process" (WSS) means that its mean is a constant, and its auto-correlation is time-invariant, that is: $$\begin{aligned}E[x(t)] &= c \\ R_X(t_1, t_2) &= R_X(...
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2answers
511 views

WSS vs SSS vs ergodic

Is this the correct "venn diagram" that related WSS, SSS, and Ergodic process types? $$\text{all process types}\begin{cases}\text{WSS} \begin{cases}SSS \begin{cases}\text{ergodic} \\ \text{...
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2answers
79 views

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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1answer
76 views

Stationarity, discrete-translation operator, and the power spectral density matrix

Let $\mathbf{T}$ be the translation operator/matrix in discrete-time domain which can be written as $\mathbf{T} = \mathbf{\Phi} \mathbf{P} \mathbf{\Phi}^*$ where $\mathbf{P} = \exp(-i Diag([w_0, w_1, \...
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1answer
76 views

Complex gaussian random variable [closed]

In my work i need to generate circularly symmetric complex gaussian random variables with non zero mean and certain variance in matlab. I know the command for generating in case of zero mean , but ...
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3answers
966 views

Autocorrelation function and correlation integral

I am confused by the definition of autocorrelation function. It is originally defined as the expected value $$R_{XX}(\tau) = E[(X(t)X(t+\tau)] = \langle X(t)X(t+\tau)\rangle\tag{1}$$ where $\langle\...
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1answer
238 views

Processes: Orthogonal, Uncorrelated, Statistically Independent

How are they all related? You can define them as: Orthogonal Processes: $E[XY] = 0$ Uncorrelated Processes: $E[XY] = E[(X - \mu_x)(Y - \mu_y)] = 0$ Statistically Independent Processes: $E[XY] = E[X] \...
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2answers
45 views

Filter Percentage Uniform Noise from a DC-signal?

I'm not good with signal processing but i've looked around and have got no clue how to approach this. My Question is, If there is a Static value present - that is being corrupted by percentage ...
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25 views

Proving that this process is weakly-stationary [duplicate]

Let $X(t) = Acos(2\pi f_c t)$ be a random process where $A$ is a uniform random variable within $(-1,1)$. I'm trying to prove this is a weakly(i.e. wide sense) stationary process. I need to show two ...
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2answers
129 views

When deriving the power spectral density of stochastic processes, why does taking an expectation allow the $T\rightarrow\infty$ limit to be taken?

I am following the arguments presented in the paper AN-255 Power Spectra Estimation, from Texas Instruments, to learn how to derive the power spectral density for a stationary stochastic process, and ...
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1answer
183 views

Blind Estimation of Signal Parameter and Noise Variance

Let $y[n]= h*x[n] + w[n]$, where $h$ is an unknown but deterministic parameter, $x[n]$ is a BPSK random variable with equal probability of +1 and -1, $w[n]$ are i.i.d. Gaussian with zero mean and ...
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1answer
185 views

Power spectrum of uniform white noise

Given a white noise image $W_{i,j} \sim U[a,b]$ where each pixel is distributed uniformly in $[a,b]$, how would I go about computing its power spectral density? That is, I want to find $E[|\hat{W}_{i,...
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1answer
33 views

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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1answer
107 views

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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2answers
97 views

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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1answer
33 views

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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1answer
60 views

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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0answers
108 views

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 ...