数字信号

下面为附件内容-----

%实验一:频谱分析与采样定理
T=0.0001;               %采样间隔T=0.0002
F=1/T;                 %采样频率为F=1/T
L=0.01;                %记录长度L=0.01  
N=L/T;                
t=0:T:L;            
a=37;
f1=0:F/N:F;
f2=-F/2:F/N:F/2;
%%%%%%%%%%%%%%%%%%%%%%%%%
x1=cos(100*pi*a*t);
y1=T*abs(fft(x1));
y11=fftshift(y1);
figure(1),
subplot(3,1,1),plot(t,x1);title('正弦信号');
subplot(3,1,2),stem(f1,y1);title('正弦信号频谱');
subplot(3,1,3),stem(f2,y11);title('正弦信号频谱');
%%%%%%%%%%%%%%%%%%%%%
x2=exp(-a*t);
y2=T*abs(fft(x2));
y21=fftshift(y2);
figure(2),
subplot(3,1,1),stem(t,x2);title('指数信号');
subplot(3,1,2),stem(f1,y2);title('指数信号频谱');
subplot(3,1,3),stem(f2,y21);title('指数信号频谱');
%%%%%%%%%%%%%%%%%%%%%
x3=x1.*x2;
y3=T*abs(fft(x3));
y31=fftshift(y3);
figure(3),
subplot(3,1,1),stem(t,x3);title('两信号相乘');
subplot(3,1,2),stem(f1,y3);title('两信号相乘频谱');
subplot(3,1,3),stem(f2,y31);title('两信号相乘频谱');

 

-----下面为附件内容-----

%实验二:卷积定理
%陈友兴
x=[3 0 2 1 3];  %原始序列
y=[3 0 2 1 3];
%直接计算圆周卷积或线性卷积
z=conv(x,y);
figure(1),subplot(311),stem(x);axis([1 8 0 4]);
subplot(312),stem(y);axis([1 8 0 4]);
subplot(313),stem(z);axis([1 8 0 30]);
%利用FFT计算
N=10;%N=8时
x1=[x zeros(1,N-length(x))];
y1=[y zeros(1,N-length(y))];
X1=fft(x1);
Y1=fft(y1);
Z1=X1.*Y1;
z1=ifft(Z1);
figure(2),
subplot(321),stem(x1);
subplot(322),stem(real(X1));
subplot(323),stem(y1);
subplot(324),stem(real(X1));
subplot(325),stem(z1);
subplot(326),stem(real(Z1));
N=5;%N=5时
x2=[x zeros(1,N-length(x))];
y2=[y zeros(1,N-length(y))];
X2=fft(x2);
Y2=fft(y2);
Z2=X2.*Y2;
z2=ifft(Z2);
figure(3),
subplot(321),stem(x2);
subplot(322),stem(real(X2));
subplot(323),stem(y2);
subplot(324),stem(real(X2));
subplot(325),stem(z2);
subplot(326),stem(real(Z2));

-----下面为附件内容-----

%实验三  IIR滤波器设计实验
%先设计模拟滤波器，再转化数字滤波器
clc;
clear all;
wp=0.2*pi;%通带内频率
ws=0.3*pi;%阻带内频率
Rp=1;%最大衰减
Rs=15;%最小衰减
Ts=0.02*pi;
Fs=1/Ts;
wp1=2/Ts*tan(wp/2);%将模拟指标转变成数字指标
ws2=2/Ts*tan(ws/2);%将模拟指标转变成数字指标
[N,Wn]=buttord(wp1,ws2,Rp,Rs,'s');  %选择滤波器的最小阶数  
[Z,P,K]=buttap(N);%创建butterworth模拟滤波器
[Bap,Aap]=zp2tf(Z,P,K)%零极点增益模型到传递函数模型的转换
[b,a]=lp2lp(Bap,Aap,Wn);%Lp2lp 低通到低通   
[bz,az]=bilinear(b,a,Fs);%用双线性变换法实现模拟滤波器到数字滤波器的转换 
[H,W]=freqz(bz,az,50);%绘制频率响应曲线求出对应范围内50个频率点的频率响应样值
L=length(W)/2+1;%数字滤波器在频率区间[0, π/2]，25个频率点的频率响应样值
figure(1),plot(W(1:L)/pi,abs(H(1:L))),grid,xlabel('角频率(/pi)'),ylabel('频率响应幅度');
    x=[-4,-2,0,-4,-6,-4,-2,-4,-6,-6,-4,-4,-6,-6,-2,6,12,8,0,-16,-38,...
-60,-84,-90,-66,-32,-4,-2,-4,8,12,12,10,6,6,6,4,0,0,0,0,0,-2,...
-4,0,0,0,-2,-2,0,0,-2,-2,-2,-2,0];
y=filter(bz,az,x);            %滤波
figure(2),
subplot(2,1,1),plot(x),title('原始信号');
subplot(2,1,2),plot(y),title('滤波后信号');

 

 

-----下面为附件内容-----

%实验四  FIR滤波器设计实验
%先设计模拟滤波器，再转化数字滤波器
clc;
clear all;
Fs=3*pi*10^4;
wp=3*pi*10^3;
ws=6*pi*10^3;
f=50;
wdelta=2*pi*(ws-wp)/Fs;
N1=ceil(8*pi/wdelta);
N2=ceil(12*pi/wdelta);
N3=ceil(10*pi/wdelta);
Wn=(wp+ws)/2;
wm=Wn/Fs/pi;
w1=hamming(N1+1)%海明窗
w2=blackman(N2+1)%布拉克曼窗
w3=kaiser(N3+1,2.5)%恺撒窗
figure(1),
b=fir1(N1,wm,w1);
freqz(b,1,512)
title('海明窗');
figure(2),
b=fir1(N2,wm,w2);
freqz(b,1,512)
title('布拉克曼窗');
figure(3),
b=fir1(N3,wm,w3);
freqz(b,1,512)
title('恺撒窗,beta=2.5');