Open Access

Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function

EURASIP Journal on Advances in Signal Processing20052005:406531

DOI: 10.1155/ASP.2005.1910

Received: 13 September 2004

Published: 28 July 2005


An efficient method for the design of nonrecursive digital filters using the ultraspherical window function is proposed. Economies in computation are achieved in two ways. First, through an efficient formulation of the window coefficients, the amount of computation required is reduced to a small fraction of that required by standard methods. Second, the filter length and the independent window parameters that would be required to achieve prescribed specifications in lowpass, highpass, bandpass, and bandstop filters as well as in digital differentiators and Hilbert transformers are efficiently determined through empirical formulas. Experimental results demonstrate that in many cases the ultraspherical window yields a lower-order filter relative to designs obtained using windows like the Kaiser, Dolph-Chebyshev, and Saramäki windows. Alternatively, for a fixed filter length, the ultraspherical window yields reduced passband ripple and increased stopband attenuation relative to those produced when using the alternative windows.

Keywords and phrases

nonrecursive digital filters FIR filters window functions ultraspherical window digital differentiators Hilbert transformers

Authors’ Affiliations

Department of Electrical and Computer Engineering, University of Victoria


© Bergen and Antoniou 2005