This module looks at the computational savings of the polyphase/DFT modulated filterbank implementation by comparing the number of computations performed for various methods.
This module will briefly take a look a the computational savings
of the polyphase/DFT modulated filterbank implementation. Wewill start by looking at our standard analysis bank and then
move on to compare this with our other implementation approaches.
Assume that the lowpass filter in the standard analysis bank,
,
has impulse response length
. To
calculate the sub-band output vector
using the standard structure, we have
where we have included one multiply for the modulator. Thecalculations above pertain to standard (
i.e. ,
not polyphase) decimation. If we implement thelowpass/downsampler in each filterbank branch with a polyphase
decimator,
To calculate the same output vector for the polyphase/DFT
structure, we have approximately
The table below gives some typical numbers. Recall that the
filter length
will be linearly
proportional to the decimation factor
, so that the ratio
determines the passband and stopband performance.
|
,
|
,
|
| standard |
328,704 |
20,987,904 |
| standard with polyphase |
10,272 |
163,968 |
| polyphase/DFT |
400 |
1,728 |
