Showing papers on "Residue number system published in 1977"

The use of residue number systems in the design of finite impulse response digital filters

Abstract: A technique is presented for implementing a finite impulse response (FIR) digital filter in a residue number system (RNS). For many years residue number coding has been recognized as a system which provides a capability for the implementation of high speed multiplication and addition. The advantages of residue coding for the design of high speed FIR filters result from the fact that an FIR requires only the high speed residue operations, i.e., addition and multiplication, while not requiring the slower RNS operations of division or sign detection. A new hardware implementation of the Chinese Remainder Theorem is proposed for an efficient translation of residue coded outputs into natural numbers. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters. An RNS implementation of a 64th-order dual bandpass filter is compared with several alternative filter structures to illustrate tradeoffs between speed and hardware complexity.

System for processing arithmetic information using residue arithmetic

Abstract: A system for processing arithmetic information wherein the residue number system is used to partition a calculation into several simpler calculations each of which can be processed in parallel with complete independence. These segments are computationally simple such that all the arithmetic interactions can be ennumerated as mathematical "mappings". By routing signals through various "mappings" a number is encoded into residue form, processed in various ways, and eventually decoded back to a normal number system. The signals are routed in a manner to reflect calculations involving a plurality of operands and operations. By routing several signals in close sequence, calculations are pipelined. By routing different types of signals independently several calculations are carried out substantially simultaneously with each other. Detection of abnormalities in the signal from a given segment is used to exclude the segment from the decoding process thus preserving the correctness of the overall calculations notwithstanding an error in part of the computation.

Hardware realization of digital signal processing elements using the residue number system.

Abstract: In the past, hardware realization of digital signal processing elements have been based upon binary arithmetic concepts. Because of the dependence between digits in binary arithmetic operations, the hardware required to construct arithmetic elements is cumbersome. In the residue number system, arithmetic operations can be performed with complete independence between digits and a corresponding reduction in hardware complexity. In fact, using current technology, arithmetic operations can be carried out using arrays of look-up tables placed in high density ROMs. This paper discusses the application of the residue number system to realizing digital signal processing elements using such arrays and advantages and disadvantages over conventional realizations are discussed. Examples are given of recursive filter and FFT butterfly element realization.

Base conversion in residue number systems

Abstract: We are concerned in this paper with the representation of an integer in a (multiple-modulus) residue number system and, in particular, with an algorithm for changing the base vector of the residue number system. Szabo and Tanaka [1, p.47] describe such an algorithm when each modulus of the second base vector is relatively prime to each modulus of the first base vector. However, we show that a much simpler algorithm exists if we allow the moduli of the second base vector to have factors in common with the moduli of the first base vector (even though the moduli of the second base vector are pairwise relatively prime among themselves). Since the algorithm involves the use of "associated" residue and mixed-radix representations for integers, Section 2 contains an elementary survey of the terminology, notation, and theory behind these two types of representation. Section 3 contains the proofs of the basic theorems upon which our algorithm for residue base conversion is based along with a description of the algorithm. It also contains illustrative examples which demonstrate the power of the algorithm. In this paper we lay the foundation for a subsequent paper in which we propose procedures for extending single-precision residue arithmetic to multiple-precision residue arithmetic.