数字信号处理DSP实验四报告

Design of a Butterworth Lowpass Digital Filter by using bilinear method
bandpass attenuation 1 dB
bandstop attenuation 40 dB
bandpass edge frequency 400 hz
bandstop edge frequency 500 hz
samling frequency 2000hz
clc;clear all
Rp = 1; % bandpass attenuation in dB 带通衰减
Rs = 40; % bandstop attenuation in dB 带阻衰减
OmegaP1_1=400; % bandpass edge frequency 带通截至频率
OmegaS1_1=500; % bandstop edge frequency 带阻截至频率
Fp=2000; % samling frequency 采样频率
Wp1=2*pi*OmegaP1_1/Fp; % change analog frequency to digital angular frequency
Ws1=2*pi*OmegaS1_1/Fp; % change analog frequency to digital angular frequency 数字参数
OmegaP1=2*Fp*tan(Wp1/2); % nonlinearlization
OmegaS1=2*Fp*tan(Ws1/2); % nonlinearlization 转换为模拟参数
Eta_P=OmegaP1/OmegaP1; % Normalization
Eta_S=OmegaS1/OmegaP1; % Normalization 归一化
Lemta_P_EquivalentLowPass=Eta_P; % change to the equivalent Lowpass patameter
Lemta_S_EquivalentLowPass=Eta_S; %% change to the equivalent Lowpass patameter 变量命名
% Estimate the Filter Order
[N, Wn] = buttord(Lemta_P_EquivalentLowPass, Lemta_S_EquivalentLowPass, Rp, Rs,'s');
% Design the Filter
[num1,den1] = butter(N,Wn,'s');
[num2,den2]=lp2lp(num1,den1,OmegaP1);
[num,den]=bilinear(num2,den2,Fp);
% Compute the gain response
w = 0:pi/255:pi;
h = freqz(num,den,w);
g = 20*log10(abs(h));
% Plot the gain response
figure;
plot(w/pi,g);grid
axis([0 1 -60 5]);
xlabel('\omega /\pi'); ylabel('Gain in dB');
title('Gain Response of a Butterworth Lowpass Filter');
00.10.20.30.40.5
0.60.70.80.91
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ω /πG a i n i n d B Gain Response of a Butterworth Lowpass Filter
Experiment:
1
Design of a Cheby1 Highpass Digital Filter by using bilinear method
bandpass attenuation 1 dB
bandstop attenuation 32 dB
bandpass edge frequency 800 hz
bandstop edge frequency 500 hz
samling frequency 2000hz
code:
clc;clear all
Rp=1;
Rs=32;
OmegaP1_1=800;
OmegaS1_1=500;
Fp=2000;
Wp1=2*pi*OmegaP1_1/Fp;
Ws1=2*pi*OmegaS1_1/Fp; %digtal freguency OmegaP1=2*Fp*tan(Wp1/2);
OmegaS1=2*Fp*tan(Ws1/2); %change into anolog frequency Eta_P=OmegaP1/OmegaP1;
Eta_S=OmegaS1/OmegaP1; %归一化
[N,Wn]=cheb1ord(1,1/Eta_S,Rp,Rs, 's ');
[B,A]=cheby1(N,1,Wn, 's ');
[BT,AT]=lp2hp(B,A,Eta_S);
[num,den]=bilinear(BT,AT,0.5); %MAYBE ERROR w = 0:pi/255:pi;
h = freqz(num,den,w);
g = 20*log10(abs(h));
figure;
plot(w/pi,g);grid
axis([0 1 -60 5]);
xlabel('\omega /\pi'); ylabel('Gain in dB');
title('Gain Response of a cheby1 highpass Filter');
results:
00.10.20.30.40.5
0.60.70.80.91
-60-50
-40
-30
-20
-10
ω /πG a i n i n d B Gain Response of a cheby1 highpass Filter
2
Design of a Cheby2 Bandpass Digital Filter by using bilinear method
bandpass attenuation 1 dB
bandstop attenuation 40 dB
bandpass edge frequency 400 hz
bandpass edge frequency 500 hz
bandstop edge frequency 350 hz
bandstop edge frequency 550 hz
code:
clc;clear all
Rp=1;
Rs=40;
Fp=2000;
OmegaP1_1=400;
OmegaP1_2=500;
OmegaS1_1=350;
OmegaS1_2=550;
Wp1=2*pi*OmegaP1_1/Fp;
Wp2=2*pi*OmegaP1_2/Fp;
Ws1=2*pi*OmegaS1_1/Fp;
Ws2=2*pi*OmegaS1_2/Fp; %digtal freguency
OmegaP1=2*Fp*tan(Wp1/2);
OmegaP2=2*Fp*tan(Wp2/2);
OmegaS1=2*Fp*tan(Ws1/2);
OmegaS2=2*Fp*tan(Ws2/2); %change into anolog frequency
Bw=OmegaP1-OmegaP2;
Bs=(OmegaS2-OmegaS1)/2;
Etap1=OmegaP1/Bw;
Etap2=OmegaP2/Bw;
Etas1=OmegaS1/Bw;
Etas2=OmegaS2/Bw;
Eta02=Etap1*Etap2;
Lmdp1=1;
Lmdp2=-1;
Lmds1=(Etas1*Etas1-Eta02)/Etas1;
Lmds2=( Eta02-Etas2*Etas2)/Etas2;
Lmdp=1;
Lmds=min(Lmds1,Lmds2); %归一化
[N,Wn]=cheb2ord(1,Lmds,Rp,Rs, 's');
[B,A]=cheby2(N,1,Wn, 's');
[BT,AT]=lp2bp(B,A ,Bs,Bw);
[num,den]=bilinear(BT,AT,2000);
w = 0:pi/255:pi;
h = freqz(num,den,w);
g = 20*log10(abs(h));
figure;
plot(w/pi,g);grid
axis([0 1 -60 5]);
xlabel('\omega /\pi'); ylabel('Gain in dB');
title('Gain Response of a cheby2 bandpass Filter');
results:
00.10.20.30.40.5
0.60.70.80.91
-60-50
-40
-30
-20
-10
ω /πG a i n i n d B Gain Response of a cheby2 bandpass Filter。