数字信号处理吴镇杨版实验二 信号的采样与重建.docx

1、数字信号处理吴镇杨版实验二 信号的采样与重建 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

2、(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,（2）输入信号X(n)为归一化频率f1=0.043，f2=0.31的两个

3、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 sequenc

4、e 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);

5、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);（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

6、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,

7、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 seq

8、uence);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);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);ste

9、m(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(1:51

10、2);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 );xl

11、abel(w);ylabel(fudu);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);fi

12、gure(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 sequ

13、ence);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);(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(

14、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);