A design method of 2D FIR fan filters for wideband beam forming by means of 2D Fourier series approximation

Abstract

AbstractIn order to realize beam forming with an identical radiation characteristic over a wide bandwidth, this paper describes a method of design for two‐dimensional FIR fan filters with wedge‐shaped transition regions. In order to provide excellent amplitude approximations in a wide range from low to high frequencies with different transition range widths, a method based on the two‐dimensional Fourier series approximation is used. The approximate amplitude characteristic of the target fan filter for which the widths of the passband and the transition band are specified in proportion to the frequency from the origin is greatly degraded at low frequencies near the origin. To reduce this degradation, the target amplitude characteristic at low frequencies of the fan filter is replaced with a rectangular cross‐sectional shape. The width of the rectangular amplitude characteristic is set such that the amplitude of the designed result takes the specified value on the center line. Design examples are given for an axially symmetric fan filter and a diagonally symmetric fan filter. Further, the characteristics of the beam formers using these filters are derived and the effectiveness of the method is demonstrated. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(7): 38–49, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1106