Linked Questions

1 vote
0 answers
63 views

A wide sense stationary random process that is not second order stationary [duplicate]

I have been reading Peebles Probability, Random Variables, and Random Signal Principles and it claims that second-order stationarity is sufficient to guarantee: $E[X(t)]$ is a constant $R_{XX}(t1,t2) ...
VMMF's user avatar
  • 1,142
6 votes
2 answers
1k views

Why is $A\cos(2\pi f_ct)$ a non-stationary process?

I am studying analog communication and having Communication system - Simon Hykin as one of the reference. There is a question Consider the sinusoidal process$$X(t) = A\cos(2\pi f_ct)$$where the ...
TIWARI's user avatar
  • 163
4 votes
4 answers
2k 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?
m-sh-shokouhi's user avatar
4 votes
2 answers
20k views

What is the difference between wide sense and strict sense stationary processes?

What is the difference between wide sense and strict sense stationary processes (SP) ? According to the definition (by Heinrich Meyr, Marc Moeneclaey, Stefan A. Fechtel in "Synchronization, Channel ...
József Hegedüs's user avatar
9 votes
1 answer
3k views

Question on covariance matrix of 2 spatial signals

Every time I think I have understood the covariance matrix, someone else comes up wih a different formulation. I am currently reading this paper: J. Benesty, "Adaptive eigenvalue decomposition ...
Spacey's user avatar
  • 9,837
-1 votes
2 answers
2k 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{...
pico's user avatar
  • 203
3 votes
1 answer
752 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(...
Andrea's user avatar
  • 539
0 votes
1 answer
2k views

white noise filtering

If I have a white noise fed into a filter what would be the output of the filter - what would you expect to see? I know that white noise has a unit power spectral density (PSD), how these thing relate ...
Lakshmi's user avatar
  • 135
-1 votes
1 answer
534 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(...
pico's user avatar
  • 203
0 votes
1 answer
358 views

PDF of a Shifted Rectangular Pulse

I wanted to determine the PDF of a Stochastic Process. I am familiar with the concept of PDF for a Random Variable which maps the outcomes to its probabilities but I am not able to find the PDF of a ...
sundar's user avatar
  • 343
1 vote
1 answer
333 views

Autocorrelation for Stationary Signals

I'm having trouble grasping the autocorrelation function for stationary signals, both strict stationary and WSS. First for strict sense, we have $$\forall(\tau,t_1, \ldots, t_n) \in \mathbb{R} \land ...
Colin Hicks's user avatar
2 votes
1 answer
264 views

Super basic questions on statistical process

Before starting: I am really a beginner in statistical process in time. I mainly do quantum information and while learning aspect of quantum noise I realized that I am actually too weak on basics of ...
StarBucK's user avatar
  • 289
1 vote
1 answer
124 views

Why is a random process strictly stationary when its joint Probability density function is time invariant?

I don't understand what stationarity of random process mean. I know they're statistical properties that are time invariant but I don't have intuition for it and I don't get what that has to do with ...
mahmoud esmail's user avatar
0 votes
1 answer
169 views

Properties of Stochastic Processes [closed]

I have a basic question about stochastic processes: When some informations such as wss, uncorraleted sampled, white about random signal (say x[n]) are given, what do we exactly have? For example ...
mehmet's user avatar
  • 161
0 votes
1 answer
148 views

How do we compute distrubtions of the value of a random process conditional on initial conditions?

Suppose I have a stationary process $\phi(t)$ with a known autocorrelation function $$ A(\tau) \equiv \langle \phi(0) \phi(\tau) \rangle$$ and suppose I also know that $\phi(t)$ is Gaussian ...
DanielSank's user avatar
  • 1,056

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