Complex random variableΒΆ
For a complex random variable \(Z = X + j Y\), its PDF is the joint PDF of the r.v. X and Y.
\[f_Z(z) = f_{X, Y} (x, y).\]
The integral over the complex space is defined as
\[\int_{z \in \CC} f_Z(z) d z = \int_{-\infty}^{\infty}
\int_{-\infty}^{\infty} f_{X, Y} (x, y) d x d y = 1.\]