A Design Method for 3-Dimensional Band-Limiting FIR Filters Using McClellan Transfromation

Toshiyuki YOSHIDA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A    No.8    pp.1283-1292
Publication Date: 1993/08/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section of Papers Selected from the 7th Digital Signal Processing Symposium)
Category: Multidimensional Signal Processing
digital signal processing,  FIR filters,  band-limiting filters,  multidimensional filters,  McClellan transformation,  

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In multidimensional signal sampling, the orthogonal sampling scheme is the simplest one and is employed in various applications, while a non-orthogonal sampling scheme is its alternative candidate. The latter sampling scheme is used mainly in application where the reduction of the sampling rate is important. In three-dimensional (3-D) signal processing, there are two typical sampling schemes which belong to the non-orthogonal samplings; one is face-centered cubic sampling (FCCS) and the other is body-centered cubic sampling (BCCS). This paper proposes a new design method for 3-D band-limiting FIR filters required for such non-orthogonal sampling schemes. The proposed method employs the McClellan transformation technique. Unlike the usual 3-D McClellan transformation, however, the proposed design method uses 2-D prototype filters and 2-D transformation filters to obtain 3-D FIR filters. First, 3-D general sampling theory is discussed and the two types of typical non-orthogonal sampling schemes, FCCS and BCCS, are explained. Then, the proposed design method of 3-D bandlimiting filters for these sampling schemes is explained and an effective implementation of the designed filters is discussed briefly. Finally, design examples are given and the proposed method is compared with other method to show the effectiveness of our methos.