Binary Polynomial Transforms for Nonlinear Signal Processing
BINARY POLYNOMIAL TRANSFORMS FOR NONLINEAR SIGNAL PROCESSING Jaakko Astola, Karen Egiazarian, Rugen oktern SOS Agaian Signal Processing Laboratory Electrical Engineering Department Tampere University of Technology University of Texas at San Antonio Tampere, FINLAND San Antonio, Texas, USA ABSTRACT ing computers or systems suitable for simultaneous arith- metical or logical operations. In this paper we introduce parametric binary Rademacher functions of two types. Based on them using different kinds 2. BINARY POLYNOMIAL FUNCTIONS AND of arithmetical and logical operations we generate a set of MATRICES binary polynomial transforms (BPT). Some applications of BPT in nonlinear filtering and in compression of binary 2.1. Rademacher Functions and Matrices images are presented. Let a and b be arbitrary integers. We form the classes r,(t,a, b) and s,(t,a, b) of real periodic functions in the 1. INTRODUCTION following way. Let Spectral analysis is a powerful tool in communication, sig- ro(t.a,b) E so(t,a, b) E 1, (1) nal/ image processing and applied mathematics and there are many reasons behind the usefulness of spectral analysis. First, in many applications it is convenient to transform a a, fortEU~~ol[$,fk++i), problem into another, easier problem; the spectral domain rn+l (t, a, b) = is essentially a steady-state viewpoint; this not only gives b, for t E U~~ol[ $t + 5&l *).2 insight for analysis but also for design. Second, and more (2) important: the spectral approach allows us to treat entire and classes of signals which have similar properties in the spec- tral domain; it has excellent properties such as fast algo- a: for t E LO,&I, n = 0, 1,2, .
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