chcoeff.m

很多matlab的源代码

function [z,y] = chcoeff(n,ty)
% CHCOEFF Coefficients of the nth order Chebyshev polynomial.
%
%	[Z,Y] = CHCOEFF(N,TY) Coeffs of an Nth order Chebyshev polynomial.  
%	TY=1 for T(n) (first kind), TY=2 for U(n) [second kind][DEFAULT: TY=1]
%	Z contains the N+1 coefficients of the Nth order polynomial. 
%	Y is a matrix whose N rows are Cheby poly. coeffs from order 1 to N.
%
%	CHCOEFF (with no input arguments) invokes the following example:
%
%       % Find coefficients of all Chebyshev polynomials T(n) to order 5.
%         >>[a,b] = chcoeff(5)


% ADSP Toolbox: Version 2.0 
% For use with "Analog and Digital Signal Processing", 2nd Ed.
% Published by PWS Publishing Co.
%
% Ashok Ambardar, EE Dept. MTU, Houghton, MI 49931, USA
% http://www.ee.mtu/faculty/akambard.html
% e-mail: [e-mail]
% Copyright (c) 1998



%We use the recursion T(n)=2*x*T(n-1) - T(n-2) with T(0)=1,T(1)=x
%For U, we have: U(n)=2*x*U(n-1) - U(n-2) BUT with U(0)=1,U(1)=2x

if nargin==0,help chcoeff,disp('Strike a key to see results of the example')
pause,[a,b]=chcoeff(5),return,end


if nargin<2,ty=1;end
if n==0,z=1;y=1;return,end
y=zeros(n+1,n+1);y(1,n+1)=1;
if ty==1,y(2,n)=1;else,y(2,n)=2;end
for k=3:n+1
pk=[2*y(k-1,2:n+1) 0]-y(k-2,:);y(k,:)=pk;
end
z=y(n+1,:);