fourier_fit.m

英文书《Digital Signal Processing with Examples in MATLAB》附带的MATLAB实例

function [y,ty]=fourier_fit(x,tx,Ny)
% [y,ty]=fourier_fit(x,tx,Ny)
%
% Frequency-limited fit (y) to data (x) not uniformly
%   spaced in time (tx).
% Inputs:
% x    =vector of data samples.
% tx   =vector of corresponding time samples.
% Ny   =number of samples in (length of) output y.
% Output:
% y  =Ny samples of the inverse DFT of x.
% ty =vector of time samples corresponding with y.
% Note: The period of y is taken to be max(tx)-min(tx).

% Error checks etc.
if length(tx)~=length(x)
    error('In fourier_fit, tx and x must have the same length.');
elseif Ny<3
    error('In fourier_fit, Ny must be >2.');
elseif max(tx)-min(tx)<=0
    error('In fourier_fit, max(tx)-min(tx) must be >0.');
end
Nx=length(x);                       % Nx= # input samples
P=max(tx)-min(tx);                  % fundamental period of series
ty=linspace(min(tx),max(tx),Ny);    % time vector for output y
Ny2=floor(Ny/2);                    % half of Ny or Ny-1
mt=col_vec(tx)*[0:Ny2];             % array of exponents
w=exp(j*2*pi*mt/P);                 % exponential factor in transform
X=row_vec(x)*w ;                    % half of the DFT components
X=[X rev(conj(X(2:Ny2)))]          % all Ny components of the DFT
y=real(ifft(X));                    % y with Ny-1 samples
y=[y y(1)];                         % y with Ny samples