Linked Questions
17 questions linked to/from Does the autocorrelation function completely describe a stochastic process?
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) ...
- 1,182
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 ...
- 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?
- 350
4
votes
2
answers
21k
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 ...
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 ...
- 9,907
-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?
$$\text{all process types}\begin{cases}\text{WSS} \begin{cases}SSS \begin{cases}\text{ergodic} \\ \text{...
- 203
3
votes
1
answer
788
views
explanation of correlation of stationary stochastic processes
I have some doubts about correlation in stationary stochastic processes.
I know that the expectation of a random variable is
$$E(x)=\int_{-\infty}^{+\infty} a f_x(...
- 549
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 ...
- 135
-1
votes
1
answer
578
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:
$$\begin{aligned}E[x(t)] &= c \\ R_X(t_1, t_2) &= R_X(...
- 203
0
votes
1
answer
372
views
PDF of a Shifted Rectangular Pulse
I wanted to determine the PDF of a Stochastic Process. I am familiar with the concept of PDF for a Random Variable which maps the outcomes to its probabilities but I am not able to find the PDF of a ...
- 343
1
vote
1
answer
342
views
Autocorrelation for Stationary Signals
I'm having trouble grasping the autocorrelation function for stationary signals, both strict stationary and WSS.
First for strict sense, we have $$\forall(\tau,t_1, \ldots, t_n) \in \mathbb{R} \land ...
- 211
2
votes
1
answer
275
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 ...
- 289
1
vote
1
answer
130
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 ...
0
votes
1
answer
170
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 ...
- 161
0
votes
1
answer
160
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 ...
- 1,076