# Questions tagged [complex-random-variable]

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### 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 $\theta \sim \mathcal U(0, 2\pi)$? ...
2k 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 $N_0/2$...
272 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 ...
2k 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 ...
344 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.
51 views

### nature of output of the addition of white noise with colord noise

I want to know that the addition of a uncorrelated time series x with a correlated time series, say y generates a time series ...
187 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 ...
54 views

### How can I add complex WGN to a complex damped signal for a specified SNR?

I want to add complex wgn to a signal for a specified SNR. I have been using the following lines: ...
44 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 ...