Cross-/ auto-correlation of time-varying signals using block pulse functions and determination of power spectral densities

Abstract

The present work proposes a method based on block pulse function ( BPF) analysis for the determination of cross-/ auto-correlation of time-varying signals. These results are used subsequently to evaluate power spectral densities ( PSD) of a few codes for communication. Two Lebesgue integrable time-varying functions are represented by means of their respective equivalent BPF spectra. The BPF spectral coefficients are used to develop positive and negative correlation matrices of an operational nature. These matrices, when combined, result in a correlation matrix that is used to determine cross-/ auto-correlation of the input functions over the entire time scale. The results thus obtained in the BPF domain are utilized to determine the PSDs of a few communication codes employing the well-known fast Fourier transform algorithm. Numerical experiments are carried out to establish the validity of the proposed method and the results are found to be in close agreement with the exact solutions