實驗報告
專業班級電科0803姓名班雙江
學號 200848360304 實驗名稱 fir數字濾波器的設計
一、實驗目的：
設計fir數字濾波器
二、實驗內容：
設計乙個帶通fir數字濾波器，設計指標：通帶衰減1db,阻帶衰減40db，通帶截止頻率：500hz，700hz；阻帶截止頻率：
400hz，800hz；抽樣頻率：2000hz。
1、使用hamming窗函式：
matlab程式：
% program p7_5_1
% design of a bandpass fir digital filter
clc;clear all;
rp = 1; % bandpass attenuation in db
rs = 40; % bandstop attenuation in db
omegap1_1=500; % bandpass edge frequency
omegap1_2=700; % bandpass edge frequency
omegas1_1=400; % bandstop edge frequency
omegas1_2=800; % bandstop edge frequency
ft=2000; % samling frequency
fp=[omegap1_1 omegap1_2];
fs=[omegas1_1 omegas1_2];
deta_p=1-10^(-rp/20);
deta_s=10^(-rs/20);
% estimate the filter order
n = kaiord(fp, fs, deta_p, deta_s, ft);
% design the filter
wn=2/ft*[omegap1_1 omegap1_2];% normalize the frequency,ft/2 correspond to pi(normalize 1 correspond pi)
b=fir1(n,wn,'bandpass',hamming(n+1));
% compute the gain response
[g, w] = gain(b,1);
% plot the gain response
plot(w/pi,g);grid
axis([0 1 -60 5]);
xlabel('\omega /\pi'); ylabel('gain in db');
title('gain response of a fir bandpass filter');
執行結果
可以看出ω/π=0.4時衰減為25.5644；ω/π=0.
5時衰減為5.0733；ω/π=0.7時衰減為5.
0624；ω/π=0.8時衰減為25.7568。
不符合設計標準。
增加n值為1000：
% program p7_5_2
% design of a bandpass fir digital filter
clc;clear all;
rp = 1; % bandpass attenuation in db
rs = 40; % bandstop attenuation in db
omegap1_1=500; % bandpass edge frequency
omegap1_2=700; % bandpass edge frequency
omegas1_1=400; % bandstop edge frequency
omegas1_2=800; % bandstop edge frequency
ft=2000; % samling frequency
fp=[omegap1_1 omegap1_2];
fs=[omegas1_1 omegas1_2];
deta_p=1-10^(-rp/20);
deta_s=10^(-rs/20);
% estimate the filter order
%n = kaiord(fp, fs, deta_p, deta_s, ft);
n=1000;
% design the filter
wn=2/ft*[omegap1_1 omegap1_2];% normalize the frequency,ft/2 correspond to pi(normalize 1 correspond pi)
b=fir1(n,wn,'bandpass',hamming(n+1));
% compute the gain response
w = 0:pi/255:pi;
h = freqz(b,1,w);
g = 20*log10(abs(h));
% plot the gain response
plot(w/pi,g);grid
axis([0 1 -60 5]);
xlabel('\omega /\pi'); ylabel('gain in db');
title('gain response of a fir bandpass filter');
w1=[0.4*pi,0.5*pi,0.7*pi,0.8*pi];
h1=freqz(b,1,w1);
g1=-20*log10(abs(h1));
執行結果：
可以看出ω/π=0.4時衰減為78.5233；ω/π=0.
5時衰減為6.0191；ω/π=0.7時衰減為6.
0191；ω/π=0.8時衰減為78.2051。
通帶衰減不符合設計標準。
2、使用hanning窗函式
% program p7_5
% design of a bandpass fir digital filter
clc;clear all;
rp = 1; % bandpass attenuation in db
rs = 40; % bandstop attenuation in db
omegap1_1=500; % bandpass edge frequency
omegap1_2=700; % bandpass edge frequency
omegas1_1=400; % bandstop edge frequency
omegas1_2=800; % bandstop edge frequency
ft=2000; % samling frequency
fp=[omegap1_1 omegap1_2];
fs=[omegas1_1 omegas1_2];
deta_p=1-10^(-rp/20);
deta_s=10^(-rs/20);
% estimate the filter order
n = kaiord(fp, fs, deta_p, deta_s, ft);
%n=1000;
% design the filter
wn=2/ft*[omegap1_1 omegap1_2];% normalize the frequency,ft/2 correspond to pi(normalize 1 correspond pi)
b=fir1(n,wn,'bandpass',hanning(n+1));
% compute the gain response
w = 0:pi/255:pi;
h = freqz(b,1,w);
g = 20*log10(abs(h));
% plot the gain response
plot(w/pi,g);grid
axis([0 1 -60 5]);
xlabel('\omega /\pi'); ylabel('gain in db');
title('gain response of a fir bandpass filter');
w1=[0.4*pi,0.5*pi,0.7*pi,0.8*pi];
h1=freqz(b,1,w1);
g1=-20*log10(abs(h1));
可以看出ω/π=0.4時衰減為26.8170；ω/π=0.
5時衰減為5.2486；ω/π=0.7時衰減為5.
2501；ω/π=0.8時衰減為26.7749。
通帶衰減與阻帶衰減均不符合設計標準。
將n值改為1000：
% program p7_5
% design of a bandpass fir digital filter
clc;clear all;
rp = 1; % bandpass attenuation in db
rs = 40; % bandstop attenuation in db
omegap1_1=500; % bandpass edge frequency
omegap1_2=700; % bandpass edge frequency
omegas1_1=400; % bandstop edge frequency
omegas1_2=800; % bandstop edge frequency
ft=2000; % samling frequency
fp=[omegap1_1 omegap1_2];
fs=[omegas1_1 omegas1_2];
deta_p=1-10^(-rp/20);
deta_s=10^(-rs/20);
% estimate the filter order
%n = kaiord(fp, fs, deta_p, deta_s, ft);
n=1000;
% design the filter
wn=2/ft*[omegap1_1 omegap1_2];% normalize the frequency,ft/2 correspond to pi(normalize 1 correspond pi)
b=fir1(n,wn,'bandpass',hanning(n+1));
% compute the gain response
w = 0:pi/255:pi;
h = freqz(b,1,w);
g = 20*log10(abs(h));
% plot the gain response
plot(w/pi,g);grid
axis([0 1 -60 5]);
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