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Discrete convolution based on polynomial residue representation

100%

Smyk R.

tom No. 63

167-173

This paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS convolution in Xilinx FPGA are also presented.

A Boolean encoding of arithmetic operations

86%

Zbrzezny A.

tom Vol. 15

177--190

In this paper we present algorithms for a Boolean encoding of four basic arithmetic operations on integer numbers: addition, subtraction, multiplication and division. Integer numbers are encoded in two's complement system as vectors of Boolean formulae, and arithmetic operations are faithfully encoded as operations on vectors of Boolean formulae.