Filterbanks with >2 Branches 2.13 2001/12/28 2005/09/30 16:24:18.604 GMT-5 Phil Schniter schniter@ee.eng.ohio-state.edu Elizabeth Chan lizychan@rice.edu Michael Haag mjhaag@rice.edu constant-Q Filter Banks filterbanks L-band M-band Multi-level multi-level filterbanks Multi-stage multilevel filterbanks This module discusses two commons ways to design "modern" filterbanks with more than two branches.

Filterbanks with >2 Branches Thus far the previous discussion on filterbanks has concentrated on "modern" filterbanks with only two branches. There are two standard ways by which the number of branches can be increased.

M-Band Filterbanks The ideas used to construct two-branch PR-FIR filterbanks can be directly extended to the M-branch case. (See Vaidyanathan and Mitra) This yields, for example, a polynomial matrix H z with M rows and M columns. For these M-band filterbanks, the sub-bands will have uniform widths 2 L radians (in the ideal case) .

M-band Filterbank

Multi-Level (Cascade) Filterbanks The two-branch PR-FIR filterbanks can be cascaded to yield PR-FIR filterbanks whose sub-band widths equal 2 k for non-negative integers k (in the ideal case). If the magnitude responses of the filters are not well behaved, however, the cascading will result in poor effective frequency-selectivity. Below we show a filterbank in which the low-frequency sub-bands are narrower than the high-frequency sub-band. Note that the number of input samples equals the total number of sub-band samples.

Multi-level (Cascaded) Filterbank

We shall see these structures in the context of the discrete wavelet transform.

P.P. Vaidyanathan Multirate Systems and Filterbanks Prentice Hall 1993 Englewood Cliffs, NJ S.K. Mitra Digital Signal Processing McGraw-Hill 2001 New York 2nd edition