A fast windowing-based technique exploiting spline functions for designing modulated filter banks

Authors:
Fernando Cruz-Roldán;Pilar Martín-Martín;José Sáez-Landete;Manuel Blanco-Velasco;Tapio Saramäki
Affiliations:
Department of Teoría de la Señal y Comunicaciones, Escuela Politécnica Superior de la Universidad de Alcalá, Alcalá de Henares, Spain;Department of Teoría de la Señal y Comunicaciones, Escuela Politécnica Superior de la Universidad de Alcalá, Alcalá de Henares, Spain;Department of Teoría de la Señal y Comunicaciones, Escuela Politécnica Superior de la Universidad de Alcalá, Alcalá de Henares, Spain;Department of Teoría de la Señal y Comunicaciones, Escuela Politécnica Superior de la Universidad de Alcalá, Alcalá de Henares, Spain;Department Finland of Signal Processing, Tampere University of Technology, Tempere, Finland
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2009

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Abstract

A very fast technique to design prototype filters for modulated filter banks without using time-consuming multivariable optimization is introduced. In the proposed method, the prototype filter is optimized by using the windowing technique, with the novelty of exploiting spline functions in the transition band of the ideal filter, instead of using the conventional brick-wall filter. A study of the optimization techniques and three different objective functions existing in the literature has been carried out, and more suitable redefinitions of these objective functions are employed to achieve as optimized prototype filters as possible. The resulting filter banks closely satisfy the perfect reconstruction property, as is illustrated by means of examples.