Browse Prior Art Database

Digital Filters

IP.com Disclosure Number: IPCOM000086065D
Original Publication Date: 1976-Jul-01
Included in the Prior Art Database: 2005-Mar-03
Document File: 3 page(s) / 34K

Publishing Venue

IBM

Related People

Nussbaumer, H: AUTHOR

Abstract

A digital filter is a filter which computes any n'th sample Yn of the filtered signal by performing an aperiodic convolution: (Image Omitted) with hi for i = 0, 1, ... N-1 being fixed coefficients defined from the desired filter characteristics, and x(n-i) being the (n-i)/th/ sample of the input signal.

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Digital Filters

A digital filter is a filter which computes any n'th sample Yn of the filtered signal by performing an aperiodic convolution:

(Image Omitted)

with hi for i = 0, 1, ... N-1 being fixed coefficients defined from the desired filter characteristics, and x(n-i) being the (n-i)/th/ sample of the input signal.

Deriving the Yn through equation (1) directly, requires in practice a large amount of computing and more particularly of multiplications. 1e

This computation workload can be reduced by operating in a transformed domain, i.e., the {h(i)} set may be converted, as well as groups of {x(n)}, into {H(k)} and {X(k)} sets by using discrete transform techniques, perform term by term multiplication C(k) = H(k) , B(k) , operate inverse transforms on {C(k)} to get {cn} sets and then combine cn terms to get Yn's. This last combination may be executed very simply as shown by Gold and Rader in "Digital Processing of Signals". For instance, a mere delay and add operation on consecutive sets {cn} may be sufficient for this operation. By doing so, the number of multiplications required is roughly divided by N at least.

Naturally, this is only valid if the computing power required for performing both direct and inverse transforms is made as small as possible. In this respect, it would be highly desirable to have a transform amenable to a Fast Transform computation technique (FFT type). For this purpose, define a transform which converts a series of 8 N terms an into a set of terms A(k) related to each other by:

(Image Omitted)

with u such that p = u.v, q being a prime number related to a pseudo-Mersene number p = 2/qr/ - 1, N being relative prime with 8, j = Square Root - 1 and 2/w/ being the partic...