%對(duì)sin信號(hào)進(jìn)行抽樣得到的結(jié)論6

clc
clear
fc=1;%sin信號(hào)的頻率
a=-4;%信號(hào)的起始時(shí)間
b=4;%信號(hào)的終止時(shí)間
ts=1/(16*fc);%為使信號(hào)能較平滑的畫(huà)出，設(shè)置的采樣時(shí)間間隔
fs=1/ts;%由上面的采樣時(shí)間間隔得到的采樣頻率
%----
f_s=fc*8;%采樣頻率是sin信號(hào)頻率的8倍,即每個(gè)sin周期取樣8個(gè)點(diǎn)
t_s=1/f_s;%由上面的采樣頻率得到的采樣時(shí)間間隔
t1=a:ts:b;%信號(hào)的持續(xù)時(shí)間
f1=-fs/2+fs/length(t1):fs/length(t1):fs/2;
z=sin(2*pi*fc*t1);%原始sin信號(hào)
z_spect=fftshift(abs(fft(z)));

t_c1=a:t_s:b;
x1=sin(2*pi*fc*t_c1);
y1=0;
for i=1:length(x1)
    y1=y1+x1(i)*sinc((t1-t_c1(i))/t_s);
end
y1_spect=fftshift(abs(fft(y1)));
%----
bu_zeros=8;%補(bǔ)0的個(gè)數(shù)
t2=a:ts:b+bu_zeros*t_s;%按補(bǔ)0的個(gè)數(shù)將信號(hào)的持續(xù)時(shí)間延長(zhǎng)
f2=-fs/2+fs/length(t2):fs/length(t2):fs/2;
t_c2=a:t_s:b+bu_zeros*t_s;

x2=[x1,zeros(1,bu_zeros)];%在抽樣值后補(bǔ)0
y2=0;
for i=1:length(x2)
    y2=y2+x2(i)*sinc((t2-t_c2(i))/t_s);
end
y2_spect=fftshift(abs(fft(y2)));

figure(1)
subplot(2,2,1)
plot(t1,z,t_c1,x1,'*black');title('(a)原始信號(hào),黑點(diǎn)為抽樣點(diǎn)');grid
subplot(2,2,2)
plot(f1,z_spect);title('(b)原始信號(hào)的頻譜');grid
subplot(2,2,3)
plot(t1,y1);title('(c)用抽樣點(diǎn)重建的信號(hào)');grid
subplot(2,2,4)
plot(f1,y1_spect);title('(d)重建信號(hào)的頻譜');grid

figure(2)
subplot(2,2,1)
plot(t1,z,t_c2,x2,'*black');title('(a)原始信號(hào),黑點(diǎn)為抽樣點(diǎn)及補(bǔ)0點(diǎn)');grid
subplot(2,2,2)
plot(f1,z_spect);title('(b)原始信號(hào)的頻譜');grid
subplot(2,2,3)
plot(t2,y2);title('(c)用抽樣點(diǎn)及補(bǔ)0點(diǎn)重建的信號(hào)');grid
subplot(2,2,4)
plot(f2,y2_spect);title('(d)重建信號(hào)的頻譜');grid