We’re rewarding the question askers & reputations are being recalculated! Read more.

Questions tagged [complex-random-variable]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
2answers
67 views

Why is there only one integration in the solution if there is two integral in the formula?

In this problem the random variable is theta and according to the formula there should be two integrations but in the solution there is only one . Nor am i able to understand the meaning of x1 and x2 ...
1
vote
1answer
98 views

Energy definition for Autocorrelation lag 0 and lag 1 for complex signals

I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix. Consider a complex input signal $x(k)=[x1,x2]^T$ and $x(k-1)=[x0,...
0
votes
0answers
51 views

How to Derive Rayleigh distribution using transformation formula

Consider a complex random variable $Z=X+\jmath Y$, where the probability density function of $X$ and $Y$ are given by $$p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} {\rm e}^{-\frac{x^2}{2\sigma^2}}\quad\mbox{...
0
votes
0answers
30 views

Low pass representation of Bandpass Random process

Can A WSS random process with non-zero mean be also represented in such form.
1
vote
1answer
32 views

Variance of function of random variable

Is their an easier way to find variance of function of random variable? Till now what I am doing is first find probability density function of (function of random variable) then integrate over range.
0
votes
4answers
78 views

What is definition of independent random variable

I wan't to ask that if E{X}=0 E{Y}=0 and E{XY}=0 then how can I verify if the two random variables are independent or not. X , Y are both continuous random variables {I am not able to recall ...
0
votes
1answer
40 views

Clarifying matrix notation from an ICA-CMN paper

In the paper I am referring (and here from citeseer), complex vectors $\mathbf{z}$ and matrix $\mathbf{M}$ were defined as follows \begin{align} {{\bf z}} &= \left[z_{1},z_{2},\ldots,z_{N}\...
1
vote
1answer
31 views

(For c-FastICA) On covariance and pseudocovariance matrix of a complex random vector

I am currently studying complex FastICA and the paper says that Suppose $\mathbf{s}$ is a $n\times1$ complex random vector. If $\mathbf{s}$ has zero mean, unit variance, and uncorrelated real and ...
2
votes
2answers
432 views

PSD of complex white gaussian noise

It may be a really simple question, but I'm not sure about this one: Given a complex white Gaussian noise process with iid real and imaginary parts and a double sided power spectral density of $N_0/2$...
8
votes
3answers
215 views

Distribution of $e^{j\theta}$

Is there a canonical or analytic expression for the probability distribution for the circularly-symmetric complex random variable $Z$: $$ Z = e^{j\theta}, $$ where $\theta \sim \mathcal U(0, 2\pi)$? ...