Design of two-dimensional digital fan filters with complex coefficients using 90-degree phase-difference network

• Published in: Electronics & communications in Japan. Part 1, Communications Vol. 70; no. 3; pp. 20 - 28
• Main Authors: Hsueh, Sung-Chu, Takahashi, Shin-Ichi, Baba, Yoshi-Aki
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 1987
• ISSN: 8756-6621; 1520-6424
• DOI: 10.1002/ecja.4410700303

In two‐dimensional digital filters with complex coefficients, design flexibility is gained and the filter order can be lowered as compared with real coefficient filters. On the other hand, in the signal theory, the concept of analytic signal is well known in connection with single side‐band amplitude modulator, which can be implemented by using a bandpass filter or a 90‐degree phase‐difference network. The latter implementation, which uses all‐pass networks, yields far better characteristics as compared with the former. The conventional fan filter with complex coefficients is designed by shifting one‐dimensional low‐pass digital filters with a cutoff frequency of 0.5 π on the real frequency axis and applying a variable transformation. In contrast, we propose a new design method of fan filters with complex coefficients that combines the approach of the forementioned 90‐degree phase‐difference network for the single sideband amplitude modulation and the theory of complex coefficient filters; i.e., two all‐pass networks with 90‐degree phase‐difference are used in the new fan filters.