A Closed-Form of 2-D Maximally Flat Diamond-Shaped Half-Band FIR Digital Filters with Arbitrary Difference of the Filter Orders

Taiki SHINOHARA  Takashi YOSHIDA  Naoyuki AIKAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.3   pp.518-523
Publication Date: 2019/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.518
Type of Manuscript: PAPER
Category: Digital Signal Processing
2-D diamond-shaped filter,  maximally flat,  half-band filter,  arbitrary different filter orders,  closed-form expression,  

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Two-dimensional (2-D) maximally flat finite impulse response (FIR) digital filters have flat characteristics in both passband and stopband. 2-D maximally flat diamond-shaped half-band FIR digital filter can be designed very efficiently as a special case of 2-D half-band FIR filters. In some cases, this filter would require the reduction of the filter lengths for one of the axes while keeping the other axis unchanged. However, the conventional methods can realize such filters only if difference between each order is 2, 4 and 6. In this paper, we propose a closed-form frequency response of 2-D low-pass maximally flat diamond-shaped half-band FIR digital filters with arbitrary filter orders. The constraints to treat arbitrary filter orders are firstly proposed. Then, a closed-form transfer function is achieved by using Bernstein polynomial.