# Connexions

You are here: Home » Content » Computational Savings of Polyphase/DFT Filterbanks

### Recently Viewed

This feature requires Javascript to be enabled.

# Computational Savings of Polyphase/DFT Filterbanks

Module by: Phil Schniter. E-mail the author

Summary: 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. We will 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, Hz H z , has impulse response length NN. To calculate the sub-band output vector y k m y k m k=0M1 y k m k 0 M 1 y k m using the standard structure, we have

M decimator outputs vector × M filter outputs decimator outputs × N + 1 multiplications filter output = M 2 N + 1 multiplications vector M decimator outputs vector × M filter outputs decimator outputs × N + 1 multiplications filter output = M 2 N + 1 multiplications vector
(1)
where we have included one multiply for the modulator. The calculations above pertain to standard (i.e., not polyphase) decimation. If we implement the lowpass/downsampler in each filterbank branch with a polyphase decimator,
M branch outputs vector × N + 1 multiplications branch output = M N + 1 multiplications vector M branch outputs vector × N + 1 multiplications branch output = M N + 1 multiplications vector
(2)
To calculate the same output vector for the polyphase/DFT structure, we have approximately
1 DFT vector × M 2 log 2 M multiplications DFT × M polyphase outputs DFT × N M multiplications polyphase output 1 DFT vector × M 2 log 2 M multiplications DFT × M polyphase outputs DFT × N M multiplications polyphase output
(3)
= N + M 2 log 2 M multiplications vector = N + M 2 log 2 M multiplications vector The table below gives some typical numbers. Recall that the filter length NN will be linearly proportional to the decimation factor MM, so that the ratio NM N M determines the passband and stopband performance.

Table 1
M=32 M 32 , NM=10 N M 10 M=128 M 128 , NM=10 N M 10
standard 328,704 20,987,904
standard with polyphase 10,272 163,968
polyphase/DFT 400 1,728

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks