Polynomial division by convolution -- up to finite terms
14 Apr 2008
07 Jul 2011)
Division of two polynomials by convolution to get up to K terms.
function [q,qc,c] = polydiv_Z(b,a,K,c)
% Polynomial division by convolution.
% Calculate inverse Z-transform (Polynomial division) up to K terms:
% q(z) = b(z)/a(z),
% b(z) = b(0) + ... + b(k)/z^k + ... + b(n)/z^n.
% a(z) = a(0) + ... + a(k)/z^k + ... + a(m)/z^m.
% q(z) = q(0) + ... + q(k)/z^k + ... + q(K)/z^K + ......
% If coefficients of b(x) and a(x) are all integers, we set c = 0,
% so that the entire process involve mostly integer multiplications.
% The round-off errors may thus be eliminated.
% This code is similar to the code by Tamer Abdelazim Mellik,
% "Calculate inverse Z-transform by long division."
% By F C Chang 04/12/08 updated 07/07/11
if nargin < 4, c = 1; end;
n = length(b); m = length(a);
b = [b,zeros(1,K-1-n+m)];
if m == 1, q = b/a; qc = b; c = a; return; end;
if c == 0, w(1) = a(1)^K; else w(1) = 1; c = 1; end;
for k = 2:K+1;
w(k) = [b(k-1),-a(min(k-1,m):-1:2)]*[w(1),w(max(2,k+1-m):k-1)]'/a(1);
qc = w(2:K+1);
q = qc;
if c == 0, c = w(1), q = qc/c; end;