Questions tagged [random-process]

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Difference in following random proccess

Let just say I understand the first process that is white noise, Process 1: If $x(n)$ is a Gaussian random variable and a process is formed from a sequence of $x(n)$ and all random variables are ...
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1answer
975 views

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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1answer
190 views

Auto correlation definition

My question has to do with the definition of auto correlation/cross-correlation for random processes. Oppenheim/Schafer (Discrete time Signal Processing, Pg. 815 (Appendix A.2),2nd ed.) define auto ...
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1answer
178 views

Ergodicity of joint process

If we have two processes and both of them are ergodic. Does this mean that the joint proces is ergodic? Or other way around? If we have the dynamics for both components of the joint process what are ...
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1answer
122 views

This is an expression for the computation of kurtosis.

However, I don't understand what the subscript '4x' or the parameter (0,0) stand for. Could anyone explain ?
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0answers
38 views

How to determine if output signals represent the same process with different unknown random inputs

This is a question about how to determine if two different output signals represent the same process with different random inputs. This is related to validating ship motion modeling. When ship motion ...
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1answer
351 views

explanation of correlation of stationary stochastic processes

I have some doubts about correlation in stationary stochastic processes. I know that the expectation of a random variable is $$E(x)=\int_{-\infty}^{+\infty} a f_x(...
3
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1answer
3k views

Deterministic / Non-deterministic Stochastic Process

Problem 6.1-6 of Probability, Random Variables, and Random Signal Principles, 4th Edition by Peebles asks If a process is defined by $X(t) = A$, where $A$ is a continuous random variable uniformly ...
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2answers
6k views

What are the statistics of the discrete Fourier transform of white Gaussian noise?

Consider a white Gaussian noise signal $ x \left( t \right) $. If we sample this signal and compute the discrete Fourier transform, what are the statistics of the resulting Fourier amplitudes?
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1answer
386 views

Power Spectrum: Definition

I am new to the study of time series. Recently I have asked a question about the covariance of real and imaginary part of a real(in time domain) stochastic time series and I have received an answer ...
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0answers
106 views

What is SNR of Signal with Additive White Gaussian Noise [duplicate]

Calculating the power of AWGN should be equal to infinity as PSD is constant and its integration is infinity over all frequencies. Hence for any signal with finite power mixed with AWGN, SNR should ...
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1answer
759 views

A special case of 2 jointly Weak-Sense Stationary (WSS) stochastic processes

I know that 3 conditions must be met in order a pair of stochastic processes $X(t)$ and $Y(t)$ to be characterized as jointly WSS: 1. $X(t)\;\; WSS$ 2. $Y(t)\;\; WSS$ 3. $R_{xy}(t_1,t_2) = R_{xy}(...
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3answers
1k views

Sum of Sine and Cosine with Random Phase as LTI System

I have the following system: Where $ {H}_{1} \left( f \right) = {H}_{2} \left( f \right) $ and $ \theta \sim U[0, 2\pi]$ independent of any other factor in the system. Given the input is identical, ...
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3answers
63k views

Variance of White Gaussian Noise

It could seem an easy question and without any doubts it is but I'm trying to calculate the variance of white Gaussian noise without any result. The power spectral density (PSD) of additive white ...
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0answers
248 views

Gauss Markov Process

I am trying to generate a random signal that represents a gyroscope drift. I know the Allan Variance characteristics of the signal (ARW, RRW, Bias Instability and Cluster Time for for Bias Instability)...

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