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4.2 Perfect reconstruction qmf

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Perfect reconstruction qmf

The system transfer function for a QMF bank is

T z H 0 z 2 H 1 z 2 4 z -1 P 0 z 2 P 1 z 2
For perfect reconstruction, we need T z z l for some l , which implies the equivalent conditions 4 z -1 P 0 z 2 P 1 z 2 z l P 0 z 2 P 1 z 2 1 4 z l 1 P 0 z P 1 z 1 4 z l 1 2 For FIR polyphase filters, this can only be satisfied by P 0 z β 0 z n 0 P 1 z β 1 z n 1 where we have n 0 n 1 l 1 2 and β 0 β 1 1 4 .

In other words, the polyphase filters are trivial, so that the prototype filter H 0 z has a two-tap response. With only two taps, H 0 z cannot be a very good lowpass filter, meaning that the sub-bandsignals will not be spectrally well-separated. From this we conclude that two-channel

It turns out that M -channel perfect reconstruction QMF banks have more useful responsesfor larger values of M .
perfect reconstruction QMF banks exist but are not very useful.
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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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