design of filterbank.

what is the procedure to design filterbank.design of filterbank.

There are 2 big class of Digital Filter Design: 1) "Classical" and 2) "Modern" approach


1) You suppose Your input signal is deterministic, then You go to simulate the

correspondent analog filter who works on the analogic signal.

There are various techiques, who is practical impossible tell here in sinthetic words.

However, the major methods are a) Impulse Invariance b) Resolution of Differential

Equation (who govern Your Analogue Filter) c) Bilinear Transform (Tustin's Method).

In general is used the Invariance to the Generical Signal too. I tell to You to see on

the great book Oppenheim's "Digital Signal Processing" .


2) You suppose that Your input signal is a Stocastic Process, then You must know

his statistics. The input signal is in genearal see how the sum of original signal and

the noise. Tipically is made the ipotesi that noise is AWGN (Additive White Gaussian

Noise) : then the know of mean value and the autocorrelation, is sufficient to have

a statistical description of Your Observed [signal + noise].

If the noise is not white but colored, You must in theory, resolve the Wiener-Hopf's

Discrete Equation to obtain the desired filter. But, it is in practice very difficulty!

So, You make ipotesi that Your Process is Regular (is satisfied the Paley-Wiener

Condition) and, under this, You project a whiting filter, in the manner that it's

output is a White Process.


The major class of filters in this case are Wiener's Filter and Kalman's Filter. In general,

exists a various type of system who go under the class of Adaptive Filter: the most

famous is the Lattice Filter (look on Haykin's "Adaptive Filter Theory").


A great book about this subject is Therrien's "Discrete random signals and statistical

signal processing".


I hope to have well interpretate Your Question. If You want know on specific, ask!

First: there is a classic book on filter bank design, search it. I remember it is about multirate filter design, as old as at 80S'.

Second: What's your application? Subband voice proceesing? Then search papers on ICASSP. Else search corresponding IEEE papers.

Thrid: From my experience, if you know why and how to design a filter, and know what's your problem, then you can design filter banks