Modular Array Structures for Design and Multiplierless Realization of Two-Dimensional Linear Phase FIR Digital Filters

Saed SAMADI  Akinori NISHIHARA  Nobuo FUJII  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.4   pp.722-736
Publication Date: 1997/04/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
multi dimensional filters,  FIR digital filters,  parallel structures,  multiplierless structures,  systolic arrays,  

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Summary: 
It is shown that two-dimensional linear phase FIR digital filters with various shapes of frequency response can be designed and realized as modular array structures free of multiplier coefficients. The design can be performed by judicious selection of two low order linear phase transfer functions to be used at each module as kernel filters. Regular interconnection of the modules in L rows and K columns conditioned with boundary coefficients 1, 0 and 1/2 results in higher order digital filters. The kernels should be chosen appropriately to, first, generate the desired shape of frequency response characteristic and, second, lend themselves to multiplierless realization. When these two requirements are satisfied, the frequency response can be refined to possess narrower transition bands by adding additional rows and columns. General properties of the frequency response of the array are investigated resulting in Theorems that serve as valuable tools towards appropriate selection of the kernels. Several design examples are given. The array structures enjoy several favorable features. Specifically, regularity and lack of multiplier coefficients makes it suitable for high-speed systolic VLSI implementation. Computational complexity of the structure is also studied.