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Title
Japanese: 
English:Explicit Formula for Predictive FIR Filters and Differentiators using Hahn Orthogonal Polynomials 
Author
Japanese: サマディ サエド, 西原 明法.  
English: Saed Samadi, AKINORI NISHIHARA.  
Language English 
Journal/Book name
Japanese: 
English:IEICE Trans. Fundamentals. 
Volume, Number, Page Vol. E90-A    No. 8    pp. 1511-1518
Published date Aug. 2007 
Publisher
Japanese:電子情報通信学会 
English:IEICE 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
File
DOI https://doi.org/10.1093/ietfec/e90-a.8.1511
Abstract An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived.The formula specifies a four-parameter family of smoothing FIR digital filters containing theSavitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders.The Hahn polynomials, which are orthogonal with respect to a discrete variable,are the main tool employed in the derivation of the formula.A recursive formula for the computation of the transfer function of the filters, which is the $z$-transform of a terminated sequence of polynomial ordinates, is also introduced.The formula can be used to design structures with low computational complexity for filters of any order.

©2007 Tokyo Institute of Technology All rights reserved.