Open Access

Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics

EURASIP Journal on Advances in Signal Processing20042004:196503

DOI: 10.1155/S1110865704403114

Received: 7 April 2003

Published: 5 October 2004


A method for the design of ultraspherical window functions that achieves prescribed spectral characteristics is proposed. The method comprises a collection of techniques that can be used to determine the three independent parameters of the ultraspherical window such that a specified ripple ratio and main-lobe width or null-to-null width along with a user-defined side-lobe pattern can be achieved. Other known two-parameter windows can achieve a specified ripple ratio and main-lobe width; however, their side-lobe pattern cannot be controlled as in the proposed method. A comparison with other windows has shown that a difference in performance exists between the ultraspherical and Kaiser windows, which depends critically on the required specifications. The paper also highlights some applications of the proposed method in the areas of digital beamforming and image processing.

Keywords and phrases

window functions ultraspherical window beamforming image processing digital filters

Authors’ Affiliations

Department of Electrical and Computer Engineering, University of Victoria


© Bergen and Antoniou. 2004