## DWT filter generator - formfilter.m

This is used in several DWT programs, please check the following blog posts for more information.

http://www.dsprelated.com/showarticle/115.php

http://www.dsprelated.com/showarticle/116.php

This program requires upsample2.m

http://www.dsprelated.com/showcode/10.php

```
% ------------------------------------------------------
% Title: formfilter.m
%
% Author: David Valencia
%
% Institution: UPIITA-IPN 2010
%
% for DSPrelated.com
%
% Published in: http://www.dsprelated.com/showcode/12.php
%
% Description: This program receives 2 basic ortogonal
% filters (one is high-pass and one is low-pass)
% the filtering level and the branch number.
% As a result it returns the equivalent filter
% of the specified branch.
%
% Dependencies: upsample2.m
% http://www.dsprelated.com/showcode/10.php
%
% Revision: v1.0a
% - Commented and translated in English
%
% For more details on this code and its implementation
% see the following blog posts:
%
% http://www.dsprelated.com/showarticle/115.php
% http://www.dsprelated.com/showarticle/116.php
%
% ------------------------------------------------------
function [hx] = formfilter(n_stages,branch,h0,h1)
p = branch;
% Seed vector
hx = 0;
hx(1) = 1;
switch n_stages
case 1
% If it is a single stage filter
% the branches are just the base filters
if mod(branch,2) ~= 0
hx = h0;
else
hx = h1;
end
case 2
% For a 2 stage filter bank, the
% equivalent filters are simply
% the convolution between the corresponding
% base filters, and one of them is upsampled
% The use of upsample2 is needed to avoid having
% a large quantitiy of zeros at the end of the vector
% which certainly difficults its usage to build a
% convolution matrix.
switch branch
case 1
hx = conv(h0,upsample2(h0,2));
case 2
hx = conv(h0,upsample2(h1,2));
case 3
hx = conv(h1,upsample2(h0,2));
case 4
hx = conv(h1,upsample2(h1,2));
otherwise
beep;
fprintf('\nFor a 2 stage filter bank there can not be a fifth branch');
end
otherwise
% For a n>2 stages filter bank, a more ellaborated
% process must be made. A series of upsamplings and convolutions
% are needed to get an equivalent vector.
for i=0:n_stages-2
q = floor(p /(2^(n_stages-1-i)));
if (q == 1)
hx = conv(hx,upsample2(h1,2^i));
else
hx = conv(hx,upsample2(h0,2^i));
end
p = mod(p,2^(n_stages-1-i));
end
% Depending on the parity of the branch number, the filter
% goes through a last convolution
t = mod(branch,2);
if(t == 1)
hx = conv(hx,upsample2(h0,2^(n_stages-1)));
else
hx = conv(hx,upsample2(h1,2^(n_stages-1)));
end
end
```

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