% Name:fre_sample_fir2.m
clear,close all;
tao=2;
N=input('Type in the length N=');
L=ceil(N/3);
k=0:N-1;
M=2*pi/N;
phai=-pi*(k)*(N-1)/N-pi/2;
H=exp(i*phai);
for n=L:N
    H(n)=0;
end
kc=fix(N/2);
for i=0:kc
    H(N-(i))=conj(H(i+2));
end
subplot(221)
stem(k,abs(H),'r.')
axis([0,N-1,0,max(abs(H))])
xlabel('Frequency *pi')
title('The frequency response of an ideal lowpass filter')
h=ifft(H,N);
subplot(222)
stem(k,h,'.'),axis([0,N-1,min(h),max(h)])
xlabel('Time index n')
title('The impulse response h(n) of an FIR filter')
subplot(223)
n=0:2*pi/512:2*pi-2*pi/512;
Hd=fft(h,512);
plot(n/(2*pi),abs(Hd))
hold on,
k=0:1/N:1-1/N;
plot(k,abs(H),'r.'),axis([0,0.5,0,1.2*max(abs(H))])
xlabel('Frequency *pi')
subplot(224)
phi=atan((imag(Hd)+eps)./(real(Hd))+eps);
plot(n/(2*pi),phi),axis([0,0.3,-pi/2,pi/2])
xlabel('Frequency *pi')