数字信号处理实验报告-信号采集与重建
实验二信号的采样与重建
一.实验目的
（1）通过观察采样信号的混叠现象，进一步理解奈奎斯特采样频率的意义。
（2）通过实验，了解数字信号采样转换过程中的频率特征。
（3）对实际的音频文件作内插和抽取操作，体会低通滤波器在内插和抽取中的作用。
二.实验内容
（1）采样混叠，对一个模拟信号Va(t)进行等间采样，采样频率为200HZ，得到离散时间信号V(n).Va（t）由频率为30Hz,150Hz,170Hz,250Hz,330Hz的5个正弦信号的加权和构成。Va(t)=6cos(60pi*t)+3sin(300pi*t)+2cos(340pi*t)+4cos(500pi*t )+10sin(660pi*t)观察采样后信号的混叠效应。
程序：clear,
close all,
t=0:0.1:20;
Ts=1/2;
n=0:Ts:20;
V=8*cos(0.3*pi*t)+5*cos(0.5*pi*t+0.6435)-10*sin(0.7*pi*t);
Vn=8*cos(0.3*pi*n)+5*cos(0.5*pi*n+0.6435)-10*sin(0.7*pi*n);
subplot(221)
plot(t,V),
grid on,
subplot(222)
stem(n,Vn,'.'),
grid
on,
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（2）输入信号X(n)为归一化频率f1=0.043，f2=0.31的两个正弦信号相加而成，N=100，按因子M=2作抽取：（1）不适用低通滤波器；（2）使用低通滤波器。分别显示输入输出序列在时域和频域中的特性。 程序：clear;
N=100; M=2;
f1=0.043; f2=0.31; n=0:N-1;
x=sin(2*pi*f1*n)+sin(2*pi*f2*n); y1=x(1:2:100);
y2=decimate(x,M,'fir'); figure(1);
stem(n,x(1:N));
title('input sequence'); xlabel('n');ylabel('fudu'); figure(2); n=0:N/2-1; stem(n,y1);
title('output sequence without LP'); xlabel('n');ylabel('fudu'); figure(3); m=0:N/M-1;
stem(m,y2(1:N/M));
title('output sequence with LP'); xlabel('n');ylabel('fudu'); figure(4);
[h,w]=freqz(x);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the input sequence'); xlabel('w');ylabel('fudu'); figure(5);
[h,w]=freqz(y1);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence without LP'); xlabel('w');ylabel('fudu'); figure(6);
[h,w]=freqz(y2);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence without LP'); xlabel('w');ylabel('fudu');
010203040
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input sequence
n
f u d u
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output sequence without LP
n
f u d u
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output sequence with LP
n
f u d u
0.5
1
1.5
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3.5
051015202530354045
50frequency spectrum of the input sequence
w
f u d u
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frequency spectrum of the output sequence without LP
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frequency spectrum of the output sequence without LP
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（3）输入信号X(n)为归一化频率f1=0.043，f2=0.31的两个正弦信号相加而成，长度N=50，内插因子为2.（1）不适用低通滤波器；（2）使用低通滤波器。分别显示输入输出序列在时域和频域中的特性。 程序：clear,
close all , N=50; L=2;
f1=0.043; f2=0.31; n=0:N-1;
x=sin(2*pi*f1*n)+sin(2*pi*f2*n); figure(1);
stem(n,x(1:N));
title('input sequence'); xlabel('n');ylabel('fudu'); y1=zeros(1,N*2); y1(1:2:N*2)=x; figure(2); m=0:N*L-1;
stem(m,y1(1:N*L));
title('output sequence ');
xlabel('n');ylabel('fudu');
y2=interp(x,L);
figure(3);
m=0:N*L-1;
stem(m,y2(1:N*L));
title('output sequence');
xlabel('n');ylabel('fudu');
figure(4);
[h,w]=freqz(x);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the input sequence'); xlabel('w');ylabel('fudu');
figure(5);
[h,w]=freqz(y1);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence'); xlabel('w');ylabel('fudu');
figure(6);
[h,w]=freqz(y2);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence '); xlabel('w');ylabel('fudu');
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n
f u d u
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output sequence
n
f u d u
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40
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100
n
f u d u
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2 2.5
3 3.5
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frequency spectrum of the input sequence
w
f u d u
00.51 1.5
2 2.5
3 3.5
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frequency spectrum of the output sequence
w
f u d u
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frequency spectrum of the output sequence
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二．（3）令x(n)=cos(2*pi*f*n/fs),其中f/fs=1/16，即每个周期内有16个点。试用MATLAB 编程实现：
1）.作M=4倍的抽取，使每个周期变成4点。程序：clear,
close all,
N=100;
M=4;
n=0:N-1;
x=cos(2*pi*n*(1/16));
stem(n,x(1:N));
title('input sequence');
xlabel('n');ylabel('fudu');
y1=x(1:4:100);
y2=decimate(x,M,'fir');
figure(2);
m=0:N/4-1;
stem(m,y1);
title('output sequence ');
xlabel('n');ylabel('fudu');
figure(3);
m=0:N/M-1;
stem(m,y2(1:N/M));
title('output sequence');
xlabel('n');ylabel('fudu');
figure(4);
[h,w]=freqz(x);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the input sequence'); xlabel('w');ylabel('fudu');
figure(5);
[h,w]=freqz(y1);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence'); xlabel('w');ylabel('fudu');
figure(6);
[h,w]=freqz(y2);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence '); xlabel('w');ylabel('fudu');
n
f u d u
n
f u d u
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output sequence
n
f u d u
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2 2.5
3 3.5
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frequency spectrum of the input sequence
w
f u d u
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2 2.5
3 3.5
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f u d u
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3 3.5
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14frequency spectrum of the output sequence
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f u d u
2）.作L=3倍的插值，使每个周期变成48点。 程序：clear, close all, N=50;
L=3;
n=0:N-1;
x=cos(2*pi*n*(1/16));
figure(1);
stem(n,x(1:N));
title('input sequence');
xlabel('n');ylabel('fudu');
y1=zeros(1,N*3);
y1(1:3:N*3)=x;
figure(2);
m=0:N*3-1;
stem(m,y1(1:N*3));
title('output sequence ');
xlabel('n');ylabel('fudu');
y2=interp(x,L);
figure(3);
m=0:5:N*L-1;
stem(m,y2(1:5:N*L));
title('output sequence');
xlabel('n');ylabel('fudu');
figure(4);
[h,w]=freqz(x);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the input sequence'); xlabel('w');ylabel('fudu');
figure(5);
[h,w]=freqz(y1);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence'); xlabel('w');ylabel('fudu');
figure(6);
[h,w]=freqz(y2);
plot(w(1:64),abs(h(1:64)));
title('frequency spectrum of the output sequence '); xlabel('w');ylabel('fudu');
n
f u d u
n
f u d u
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n
f u d u
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2 2.5
3 3.5
frequency spectrum of the input sequence
w
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frequency spectrum of the output sequence
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frequency spectrum of the output sequence
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(4).输入信号x(n)为归一化频率分别是f1=0.04,f2=0.3的正弦信号相加而成，N=50,内插因子为5，抽取因子为3,给出按有理因子5/3做采样率转换的输入输出波形。 程序：clear, close all,
N=50;
M=3;
L=5;
f1=0.04;
f2=0.3;
n=0:N-1;
x=sin(2*pi*f1*n)+sin(2*pi*f2*n);
y=resample(x,L,M);
figure(1);
stem(n,x(1:N));
title('input sequence');
xlabel('n');ylabel('fudu');
figure(2);
m=0:N-1;
stem(m,y(1:N));
title('output sequence ');
xlabel('n');ylabel('fudu');
figure(3);
[h,w]=freqz(x);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the input sequence'); xlabel('w');ylabel('fudu');
figure(4);
[h,w]=freqz(y);
plot(w(1:512),abs(h(1:512)));
title('frequency spectrum of the output sequence '); xlabel('w');ylabel('fudu');