Circuit design from optimal wavelet packet series expressions

Circuit design from word-level expressions is suitable for fast prototyping, FPGA design, and software realizations. In this approach, the optimization of a circuit realizing a given function consists in selecting a basis for series expressions providing for minimum number of non-zero coefficients. The selection is performed over a variety of expressions defined in terms of different basis functions. We propose the opposite approach consisting in constructing a particular basis for each given function assuring the minimum number of non-zero coefficients. The construction of the basis is performed by exploiting principles of wavelet packets theory. Experimental results over benchmark and randomly generated functions show that the method provides considerable saving of hardware.