This work offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. The book also: introduces the Rademacher logical functions; considers fast algorithms for computing Rademacher and polynomial logical functions; focuses attention on general auto- and cross-correlation functions; and more.;The work is intended for applied mathematicians; electrical, electronics and other engineers; computer scientists; and upper-level undergraduate and graduate students in these disciplines.
Part 1 Binary polynomial transforms: binary polynomial arithmetical and logical functions and matrices; fast algorithms and complexity of binary polynomial transforms; logical correlations and binary polynomial transforms. Part 2 Binary polynomial transforms and digital logic: spectral methods in analysis of Boolean functions; spectral methods in minimization of Boolean functions. Part 3 Applications in nonlinear digital filtering: median and order statistic filters; weighted order statistic and stack filters; statistical properties of stack filters.