A new general expression for 2-channel FIR paraunitary filterbanks

Authors:
M. Elena Domínguez Jiménez
Affiliations:
Dept. Matemática Aplicada, E.T.S.I. Industriales, Universidad Politécnica de Madrid, C/José Gutiérrez Abascal, 2, 28006 Madrid, Spain
Venue:
Signal Processing
Year:
2008

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Abstract

This paper provides a new explicit expression for all real FIR paraunitary filters. From this we derive a new procedure for the design of the L components of any 2-channel FIR orthogonal L-tap filter. The input of this algorithm is any set of L/2 free parameters. Moreover, our procedure provides a parameterization of all orthogonal filters directly, with no need for iterations. For the special case of low-pass paraunitary filters, we obtain a fast new design algorithm. Simplified expressions for the frequency response of paraunitary filters are also provided. In addition to these improvements, our results also yield exact solutions of a particular set of Bezout polynomial equations.