[music-dsp] What is a "filterbank" exactly?

Sampo Syreeni decoy at iki.fi
Fri Apr 9 18:46:26 EDT 2004

On 2004-04-09, Richard (UK] uttered:

>Is this where a signal feeds into N parallel bandpass IIR/FIR filters
>followed by a summer?

Not quite. A filterbank is basically a parallel array of whatever LTI
filters you need. The summer isn't part of the description -- the term
is used both when you want to go from one signal to multiple LTI
filtered copies of it, and when you want to combine multiple signals via
LTI filters to a single target. Only in the latter case would you use a
summer. The first case is typically called an "analysis filterbank", and
the latter a "synthesis one".

The concept of a "filterbank" is significant because sometimes we can
implement the set of parallel filters in a monolithic fashion, and more
efficiently than the individual filters combined. In this case no set of
parallel filters is seen in the code we write, but just one, big,
nasty-looking filter with multiple inputs/outputs and an unusually low
computational load.

When such filters employ interpolation and decimation steps, yet still
implement a regular set of parallel filters, we call the whole thing a
"polyphase filterbank".

(I know the last part is highly imperfect, but I think it's good enough
for a FAQ answer. Do copy the above to the Wiki and improve upon it.)

>And suppose I wanted to, say, put AGC into each filter band, what
>architecture would then be most suitable?

AGC isn't linear or time-invariant (L/TI) like filterbanks or individual
filters are. If you want to use it, by all means, but the result isn't
typically called a filterbank.

It might be called a "multiband compressor" or something like that,
though. Such structures are commonly employed in loudness maximization
and noise reduction algorithms.
Sampo Syreeni, aka decoy - mailto:decoy at iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2

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