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### How to implement the filter give in Z transform using matlab

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```Good morning to every one. . .

I am very new to this forum and not much expert in DSP field too. . .

I am trying to implement a IEEE paper named "A New Delayless Subband
Adaptive Filtering Algorithm for Active Noise Control Systems"
published in IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE
PROCESSING july 2009.

I have not done any such projects before and so i am strugling where
to start and how to implement the given details.

This project is all about the following

1) A full-band =EF=AC=81lter that =EF=AC=81lters the input signal.
2) Decomposition of input and error signals into subbands.
3) Decimation in subbands.
4) Adaptive =EF=AC=81lters working in subbands.
5) A weight stacking method to combine all subbands weights into a
full-band =EF=AC=81lter.

These are the details of a filter specification given in the paper.

x(n) is the input signal which is to be filtered into M subbands named

X'k(n)

where K ranges form 0 to M-1, using a analysis filter bank h(z) with a
decimation factor D.

Filter h(z) is given by

h(z)=3D[ H0(z) ]
| H1(z) |
| . |
| . |
| . |
[ Hm-1(z)]

Where Hk(z) is the transfer function of Kth subband.

Given the low pass prototype filter for filter banks is

H0(z)=3D1+(Z)^-1+(Z)^-2+.......+(Z)^-M+1

The resulting filter bank is the simplest FIR filter perfect
reconstruction filter bank which is made by

Hk(z)=3DH0(z.exp(-j*2*pi*k/M))

with a frequency response of

H0(exp(jw))=3D{ M , when w=3D0;
{exp(-j*w(M-1)/2sin(wM/2)/sin(w/2)) , otherwise;

M is given about to be 16

D=3DM/4

For this proposed UDFT modulated filter banks, h(z) is defined by

h(z) =3D (1/M)F*[1 , (Z)^-1 , (Z)^-2 ,. . ., (Z)^-M+1] (transpose)

Where F is the DFT matix of order M. The central frequency of bandpass
filters Hk(Z) are located at

wk=3D2*pi*k/M for 0 =E2=89=A4 k =E2=89=A4 M-1.

This filter can be realized by tapped delay line of length M followed
by an inverse FFT block.
```
 0
Reply rraj.be (7) 1/30/2010 1:08:33 AM

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