In this section, for jointly SC processes, the bifrequency cross-periodogram is defined and its expected value (Lemma 3.1) and covariance (Lemma 3.2) are derived. Moreover, the bifrequency cross-periodogram is shown to be an estimator of the bifrequency spectral cross-correlation density function asymptotically biased (Theorem 3.1) and with nonzero asymptotic variance (Theorem 3.2).
Definition 4.4.1 Given two stochastic processes and , their bifrequency cross-periodogram is defined as
where and are the short-time Fourier transforms (STFTs) of y(t) and x(t), respectively, defined according to
with Z(f) denoting the (generalized) ...