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Tightening the IFFTs

In this example the top band is not downsampled at all, and
the interior bands are oversampled by approximately 2. This is because
the desired pass-band widths started out at a power of 2, so that the
addition of transition bands forced the next higher power of 2 for the
IFFT size. Narrowing the width of the top band from 121 bins to
bins would enable use of a length 128 IFFT for
the top band, and similarly for the lower bands. In other words, when
the desired spectral partition is that of an ideal octave filter bank,
as sketched in Fig.10.31, narrowing each octave-band by
twice the transition width of the lowpass prototype filter (and
``covering down'' to keep them adjacent) will produce a relatively
``tight'' FFT filterbank design in which the IFFT sizes remain the
same length as in the heavily aliased case discussed above
(Fig.10.35).
When applied to the octave filter bank, the pass-bands become a little
narrower than one octave. We may call this a *quasi octave
filter bank*.

**Next Section:**

Example: Downsampling by 2

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Simulation Results