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MATLAB软件实现计算有限长序列的DFT和IDFT函数的程序

1.编写计算有限长序列的DFT和IDFT函数
DFT的函数：
function[g,h]=dft(x,N)
n=0:N-1;k=0:N-1;
WN=exp(-j*2*pi/N);
nk=n'*k;
WNnk=WN.^nk;
X=x*WNnk;
g=abs(X);
h=angle(X)
IDFT的函数：
function [g,h]=idft(X，N);
n=0:N-1;k=0:N-1;
WN=exp(j*2*pi/N);
nk=n'*k;
WNnk=WN.^nk;
x=(X*WNnk)/N;
g=abs(x);
h=angle(x)

2.计算x=[-3 -2 3 4 2 -1 -1  2 4 3 -2 -3]
A．DFT
x=[-3 -2 3 4 2 -1 -1 2 4 3 -2 -3];N=12;
>> [g,h]=dft(x,N);
h =
  Columns 1 through 6 
         0   -2.8798   -2.6180    0.7854    1.0472    1.3090
  Columns 7 through 12 
1.4601   -1.3090   -1.0472   -0.7854    2.6180    2.8798
subplot(211);stem(g);
>> subplot(212);stem(h)
B
figure;
x=[-3 -2 3 4 2 -1 -1 2 4 3 -2 -3];N=12;
n=0:N-1;
k=0:800;w=(pi/400)*k;
Xw=x*(exp(-j*pi/400)).^(n'*k);
k1=0:N-1;
WN=exp(-j*2*pi/N);
nk=n'*k1;
WNnk=WN.^nk;
X=x*WNnk;
g=abs(X)
h=angle(X)

subplot(211);
plot(w,g);
xlabel('频率');ylabel('幅度');title('12点DTFT幅度谱');
hold on;
plot([0:11]*2*pi/12,g,'o')
subplot(212);
plot(w,h);
xlabel('频率');ylabel('相位');title('12点DTFT相位谱');
hold on;
plot([0:11]*2*pi/12,h,'o');

g =

  Columns 1 through 6 
    6.0000   10.0382   19.0526    4.2426    3.0000    2.6897
  Columns 7 through 12
    0.0000    2.6897    3.0000    4.2426   19.0526   10.0382
h =
  Columns 1 through 6 
         0   -2.8798   -2.6180    0.7854    1.0472    1.3090
  Columns 7 through 12 
    1.4601   -1.3090   -1.0472   -0.7854    2.6180    2.8798