DFS

matlab计算时，选一个主区间计算

function [Xk] = dfs(xn,N)
% Compute DFS
% Xk = DFS coeff. array over 0<=k<=N-1;
% xn = One period of periodic signal over 0<=n<=N-1;
% N = Fundamental period of xn
n = [0:1:N-1];
k = [0:1:N-1];
WN = exp(-1j*2*pi/N);
nk = n'*k;
WNnk = WN.^nk;
Xk = xn * WNnk;
end

function [xn] = idfs(Xk,N)
% Compute DFS
% Xk = DFS coeff. array over 0<=k<=N-1;
% xn = One period of periodic signal over 0<=n<=N-1;
% N = Fundamental period of xn
n = [0:1:N-1];
k = [0:1:N-1];
WN = exp(-1j*2*pi/N);
nk = n'*k;
WNnk = WN.^(-nk);
xn = (Xk * WNnk)/N;
end

clear all, close all, clc;

xn = [0,1,2,3];
N = 4;
xk = dfs(xn,N)
xn_1 = idfs(xk,N)