Use of Markov Chains for Spectral Shaping

Spectral shaping of spread spectrum signals may be desired for a variety of reasons, such as interference avoidance or increased coverture of communications. Since data are being transmitted via a digital bit stream, spectral shaping may be accomplished by adding correlation to the baseband data stream utilizing a simple shift register structure. Arbitrary spectral shaping, however, requires sophisticated techniques; Markov theory provides a rigorous mathematical foundation for the investigation of such proposed new shaping techniques. The problem of arbitrary spectral shaping via Markov chains is addressed in detail with corresponding power spectral densities plotted.