Computation of generalized FIR filter structure using the modified quadratic residue number system

1992 ◽  
Vol 39 (1) ◽  
pp. 58-62 ◽  
Author(s):  
R. Krishnan ◽  
G.A. Jullien ◽  
W.C. Miller
Keyword(s):  
Number System ◽  
Residue Number System ◽  
Quadratic Residue ◽  
Fir Filter ◽  
Filter Structure ◽  
Residue Number

EFFICIENT RNS-BASED DESIGN OF PROGRAMMABLE FIR FILTERS TARGETING FPL TECHNOLOGY

2005 ◽  
Vol 14 (01) ◽  
pp. 165-177 ◽  
Author(s):  
JAVIER RAMÍREZ ◽  
UWE MEYER-BÄSE ◽  
ANTONIO GARCÍA
Keyword(s):  
High Performance ◽  
Digital Signal ◽  
Number System ◽  
Low Complexity ◽  
Residue Number System ◽  
Quadratic Residue ◽  
Fir Filter ◽  
Efficient Implementation ◽  
Fir Filters ◽  
Residue Number

FIR filters are routinely used in the implementation of modern digital signal processing systems. Their efficient implementation using commercially available VLSI technology is a subject of continuous study and development. This paper presents the residue number system (RNS) implementation of reduced-complexity and high-performance FIR filters, using modern Altera APEX20K field-programmable logic (FPL) devices. Index arithmetic over Galois fields and the Quadratic Residue Number System (QRNS), along with a selection of a small wordwidth modulus set, are the keys for attaining low complexity and high throughput in real and complex FIR filters. RNS–FPL merged FIR filters demonstrated its superiority when compared to 2C (two's complement) filters, being about 65% faster and requiring fewer logic elements for most study cases. Special attention was paid to an efficient implementation of the multi-operand modulo adders. The replacement of a classical modulo adder tree by a binary adder with extended precision followed by a single modulo reduction stage reduced area requirements by 10% for a 32-tap FIR filter. On the other hand, an index arithmetic QRNS-based complex FIR filter yielded up to 60% performance improvement over a three-multiplier-per-tap 2C filter, while requiring fewer LEs for filters having more than eight taps. Particularly, a 32-tap filter needed 24% LEs less than the classical design.

scholarly journals Constant-coefficient FIR filters based on residue number system arithmetic

2012 ◽  
Vol 9 (3) ◽  
pp. 325-342 ◽  
Author(s):  
Negovan Stamenkovic ◽  
Vladica Stojanovic
Keyword(s):  
Power Dissipation ◽  
High Speed ◽  
Finite Impulse Response ◽  
Number System ◽  
Residue Number System ◽  
Fir Filter ◽  
Fir Filters ◽  
Residue Number ◽  
Low Power Dissipation ◽  
Residue Arithmetic

In this paper, the design of a Finite Impulse Response (FIR) filter based on the residue number system (RNS) is presented. We chose to implement it in the (RNS), because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC) unit. The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.

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