recur.m

基于WEB与MATLAB编写的信号处理的源码,书名为"应用WEB和MATLAB的信号与系统基础.

function y = recur(a,b,n,x,x0,y0);
%
% y = recur(a,b,n,x,x0,y0)
%  solves for y[n] from:
% y[n] + a1*y[n-1] + a2*y[n-2]... + an*y[n-N]
%   =  b0*x[n] + b1*x[n-1] + ... + bm*x[n-M] 
%
% a, b, n, x, x0 and y0 are vectors
% a = [a1 a2 ... aN]
% b = [b0 b1 ... bM]
% n contains the time values for which the solution will be computed
% y0 contains the initial conditions for y, in order,
%    i.e., y0 = [y[n0-N], y[n0-N+1], ...,y[n0-1]]
%    where n0 represents the first element of n
% x0 contains the initial conditions on x, in order
%    i.e., x0 = [x[n0-M],...,x[n0-1]]
% the output, y, has length(n)
%
N = length(a);
M = length(b)-1;
if length(y0) ~= N,
  error('Lengths of a and y0 must match')
end
if length(x0) ~= M,
  error('Length of x0 must match length of b-1')
end
y = [y0 zeros(1,length(n))];
x = [x0 x];
a1 = a(length(a):-1:1);             % reverses the elements in a
b1 = b(length(b):-1:1);       
for i=N+1:N+length(n),
  y(i) = -a1*y(i-N:i-1)' + b1*x(i-N:i-N+M)';
end
y = y(N+1:N+length(n));