Questions tagged [complex-random-variable]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
0answers
42 views

Detecting complex signal within complex AWGN using Neyman Pearson statistic

I need to construct a Neyman Pearson statistic for detecting a complex signal with known amplitude and unknown phase in additive complex Gaussian noise. My hypotheses are: \begin{align} \mathcal{H}_0 &...
3
votes
2answers
141 views

Signal with Complex Gaussian noise

If I have: $$ y = x_r+jx_i + n_r +j n_i$$ with $n_r$ and $n_i$ Gaussian with mean 0 and variance $\sigma^2$, what is the pdf of the envelope |y| and phase(y)? Is it still Rayleigh-distributed and ...
1
vote
1answer
67 views

Characteristic function of a random Gaussian variable

I have to find the characteristic function of a random Gaussian variable of $$ \sigma_z (w) = E e^{i w z } $$. This is the variable and I know , from the theory that the characteristic function of ...
0
votes
0answers
27 views

Calculating average power of a discrete random signal with complex values

I have a Rayleigh channel that transmits discrete values according to the following: $$y(n) = h(n) * s_n + \omega_n$$ Where $y$ is the received message, $s_n$ is the symbol sent (constellation 2-PSM), ...
0
votes
0answers
26 views

I want to invert my fourier transform components to waves again

Hi I am using R to analyze some data I basically did fft(data) and got a vector of complex numbers but from that now I want to remove certain harmonics from my actual wave but how do I convert one of ...
1
vote
1answer
144 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
2answers
116 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
44 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
105 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 ...
1
vote
1answer
36 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
1k 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 $N_0/2$...
0
votes
1answer
46 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}\right]^...
7
votes
3answers
234 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 $\theta \sim \mathcal U(0, 2\pi)$? ...