A maximally flat filter design algorithm for quadrature mirror filters (QMF)

This paper describes a numerical procedure for designing maximally flat quadrature mirror filters (QMF) for use in split-band voice coding systems. As originally proposed by Croisier, et al, the FIR filters used in QMF structures must possess certain characteristics in order to achieve perfect reconstruction of a decomposed signal (1). These constraints require that the elementary filter response exhibit an odd symmetric property about the quarter-band frequency and the 3 dB point. In addition, the filter must exhibit highly attenuated stop bands in order to orthogonalize the adjacent subbands. A filter design algorithm proposed by Herrman has been implemented and structured to satisfy these QMF constraints (2). A detailed analysis of this maximally flat FIR approach to QMF design will be discussed along with the problems associated with its implementation.