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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-frequencysub-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.

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Source:  OpenStax, Digital signal processing (ohio state ee700). OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10144/1.8
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