# Calculates inverse Z-transform by long division

### Tamer Mellik (view profile)

29 May 2002 (Updated )

Calculates inverse Z-transform by long division.

funresult=ldiv(a,b,N)
```%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Function (ldiv) : calculate inverse Z-transform by long division
% Author : Tamer mohamed samy abdelazim Mellik
% Contact information :
%Department of Electrical & Computer Engineering,
%University of Calgary,
%2500 University Drive N.W. ,
%Calgary, AB T2N 1N4 ,
% email :abdelasi@enel.ucalgary.ca
% email : tabdelaz@ucalgary.ca
% Webpage : http://www.enel.ucalgary.ca/~abdelasi/
% Date    : 2-5-2002
% Version : 1.0.0
%Example
% This function like deconv but it help if the numerator less or equal degree of denominator
% if you have this function (It must arranged in terms of minus power of Z):
%              1
% G(z)= -----------------
%             -1     -2
%      ( 5 - Z  - 3 Z  )
% and you want to calculate long division or inverse Z transform :
% The numerator  is a=[1] and  the denominator is b= [5 -1 -3 ]
% call the function ldiv(a,b) to get the funresult 20 items (default)
% another example :
%                -2     -3
%       ( 5 - 3 Z  + 4 Z  )
%  G(z)-----------------
%              -1     -2
%        (5 - Z  - 3 Z )
% a=[5 0 -3 4] , b= [5 -1 -3 ] and you want the funresult 100 terms !
% ldiv(a,b,100)
% Note : The author doesn't have any responsibility for any harm caused by the use of this file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function funresult=ldiv(a,b,N)
%a numerator
%b denominator
%default order of the filter == 20
funresult=[];
if nargin < 3
if nargin > 1
N=20;
else
disp('Usage: M = ldiv(a,b,N)')
disp('a:numerator , b denominator and N is the order of the resultant filter')
return
end
end

if size(a) < 1
disp('Error: numerator must at least have one element not empty')
return
end
if size(b) < 1
disp('Error: denominator must at least have one element not empty')
return
end

if b(1)==0
disp('Error: The first element of denominator must have nonzero value')
return
end
if size(b) < 2
funresult=a./b;
for i =length(funresult)+1:N
funresult(i)=0;
end
return
end

for i = length(a)+1:N
a(i)=0;
end
for i = 1 : N
funresult(i)=a(1)/b(1);
if length(a)>1
for k= 2:length(b)
if k > length(a)
a(k)=0;
end
a(k)=a(k)-funresult(length(funresult))*b(k);
end

for i = 1:length(a)-1
a(i)=a(i+1);
end
a=a(1:length(a)-1);
end
end

```