Questions tagged [stochastic]
The stochastic tag has no usage guidance.
10
questions
6
votes
2answers
773 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 ...
5
votes
3answers
2k views
Power Spectral Density of Brownian Motion despite non-stationary
Note: I originally asked this on Physics Stack Exchange but haven't attracted any interest there so I'm asking here where it may be more relevant.
A white noise process, $\xi(t)$ with delta ...
5
votes
1answer
3k views
Understanding of Random Process, Random Variable and Probability Density Function
I just wanted to confirm my understanding of a Random Process, Random Variable and the its Probability density Function.
Here is the way that I looked a Random Process/Random Variable:
If we ...
4
votes
2answers
2k views
What's the meaning of ergodicity? [duplicate]
I just read the topic about Ergodicity but I have ambiguity about its meaning (by intuition). What does mean: (for mean) Statistical average = Time average. Could you please explain it in detail. ...
3
votes
1answer
440 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
$$E(x)=\int_{-\infty}^{+\infty} a f_x(...
3
votes
1answer
888 views
Average Power Spectral Density of PAM signals
I am reading through the PAM transmission scheme and about the power spectral density of the signals. Given that the Average Power Spectral Density of PAM Signals is:
$$
\Phi_{ss}(f)=\Phi_{aa}\left(e^...
0
votes
1answer
3k views
Autocorrelation: numpy versus FFT
I have a series a of values (0 and 1) coming from a Brownian process with drift for which I am studying the autocorrelation.
I used two methods:
1) numpy autocorrelation:
...
0
votes
0answers
3k views
Generate time-domain random signal from PSD
Given an analytical description of the PSD, for example (MATLAB "pseudocode"):
...
0
votes
1answer
122 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 ...
0
votes
2answers
653 views
Why look at power spectral density for stochastic processes?
I have been told that for deterministic signals, it makes sense to look at their respective Fourier transforms/spectra.
For stochastic processes on the other hand, I am supposed to work with power ...
