Digital implementations of spectral correlation analyzers

The issues involved in the design of computationally efficient algorithms for spectral correlation estimation and the resulting impact on high-speed digital realization are addressed. The spectral correlation analyzer is characterized as a periodically time-varying quadratic system with a kernel possessing certain gross properties. The mean and variance of the output are expressed in terms of the kernel and the spectral correlation function of the input. Three realizations are analyzed in detail. One is based on the frequency-smoothing method of cross spectral analysis. The others are variants of the time-smoothing method. For each of these realizations, an exact expression for the quadratic system kernel is given, the digital implementation is developed, and a detailed complexity analysis is presented. High-speed pipeline realizations of the algorithms are analyzed, and related special issues are discussed. Examples involving the calculation of the spectral correlation function in near-real-time for broadband communications signals are discussed