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Comparison of Three Pipelining Recursive Digital Filters

IP.com Disclosure Number: IPCOM000060671D
Original Publication Date: 1986-Mar-01
Included in the Prior Art Database: 2005-Mar-08
Document File: 3 page(s) / 33K

Publishing Venue

IBM

Related People

Sinha, B: AUTHOR

Abstract

Three functional techniques for pipelining recursive digital filters are compared on the basis of the complexity of the pole-producing section, the number of superfluous poles which must be cancelled by zeros, the stability of the superfluous poles, and the capability of realizing arbitrary transfer functions. These techniques are: (1) Frequency Sampling, (2) Time Domain, and (3) Z-Domain. Pipelining, used to speed up any non-recursive computing operation requiring more than one operation, consists of placing registers after each processing element. Its operation is performed on each clock cycle passing the result onto the next processing element. The maximum sampling rate of a pipelined Finite Impulse Response (FIR) digital filter is completely determined by the slowest processing unit.

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Comparison of Three Pipelining Recursive Digital Filters

Three functional techniques for pipelining recursive digital filters are compared on the basis of the complexity of the pole-producing section, the number of superfluous poles which must be cancelled by zeros, the stability of the superfluous poles, and the capability of realizing arbitrary transfer functions. These techniques are: (1) Frequency Sampling, (2) Time Domain, and (3) Z- Domain. Pipelining, used to speed up any non-recursive computing operation requiring more than one operation, consists of placing registers after each processing element. Its operation is performed on each clock cycle passing the result onto the next processing element. The maximum sampling rate of a pipelined Finite Impulse Response (FIR) digital filter is completely determined by the slowest processing unit. In most binary FIR filters, this would most likely be the multiplier unit. Pipelining has also been applied effectively to table look-up FIR filters using Residue Number System (RNS) arithmetic. However, for In finite Impulse Response (IIR) filters, pipelining is less successful because the IIR filter requires feedback of the output signal. Any delay in the production of the output signal lowers the processing rate. Therefore, IIR filters tend to require sampling rates three to five times slower than equivalent FIR filters. The three techniques discussed (frequency sampling, time domain and Z-domain) allow the extension of pipelining to IIR digital filters, so as to substantially increase the sampling rates. Frequency sampling techniques for pipelining IIR filters is based on the criteria of equally spaced poles N, placed in a circle with radius r, created in a z-plane, as shown in the figure. The frequency sampling technique has the simplest pole-producing section consisting of one scaling multiplier. It has N-1 superfluous pole-pairs for each desired pole location, at an angle of f/N radians. If N is small, then the number of superfluous poles is small; however, for many desired poles, N must be large so as to obtain an approximation to the correct pole angle. This can lead to a large number of superfluous poles. Regarding stability, the frequency sampling technique generates poles with a radius equal to the desired poles; therefore, it is stable. Regarding the capability of realizing any desired filter function, the frequency sampling technique can only approximate pole angles not given by f/N, where N is an integer. Time domain technique is based on the modification...