Time-Frequency Analysis and Synthesis of Linear Signal Spaces

This text consists of nine chapters. Chapters 2-6 form a coherent part of the book, with Chapter 4 being the cornerstone of the approach of designing signal processing methods for which time-frequency considerations provide the guiding principles. The problem of synthesizing linear signal spaces is solved: with a given region in the time-frequency plane there is associated the linear signal space whose Wigner distribution is closest to the indicator function of the region. The results of Chapter 4 find ample application in Chapters 5 and 6, in which linear signal spaces with prescribed time-frequency localization are required for a variety of signal processing problems. The notion of ambiguity function of a linear signal space is introduced and applied to the problem of optimally designing a set of radar pulses. Here, "optimal" refers to minimum Cramer-bound and maximum global accuracy of the maximum likelihood multipulse estimator for range and Doppler shift.