%零相移帶通濾波器

clc

close all

clear all

% 濾波器設計

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

N = 100;%100秒

t = 0:0.001:N;%時間

Fs = 1000;%采樣率

% 濾波器通止參數設定；

fp=[0.1 15];

fs = [0.05 50];

rp = 1.5;

rs = 12;

wp = fp*2*pi/Fs;

ws = fs*2*pi/Fs;

% 階次；

[n,wn] = buttord(wp/pi,ws/pi,rp,rs);

% 濾波器系數與輻頻響應；

[b,a] = butter(n,wp/pi);

[h,w] = freqz(b,a,256,Fs);

h = 20*log10(abs(h));

figure(1)

plot(w,h);grid;ylabel('Bandpass DF');xlabel('Hz');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%信號的產生

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

f1 = 0.001;%準直流

f2 = 5;%有用信號，取1Hz到10Hz之間

f3 = 50;%工頻干擾

x1 = 100+10*sin(2*pi*f1*t);

x2 = 10*sin(2*pi*f2*t);

x3 = 10*sin(2*pi*f3*t);

figure(2)

subplot(3,1,1)

plot(t,x1);grid;

subplot(3,1,2)

plot(t,x2);grid;

subplot(3,1,3)

plot(t,x3);grid;

figure(3)

x = x1+x2+x3;

plot(t,x);grid;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

w_d = 200;

M = 1;%數據起始點%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%問題所在%%%%%%%%%%%%%%%%%%%%%%%%%%%

xn = x(M:80*w_d+M);%取x中一段數據xn

figure(4)

plot(xn);

n0 = length(xn);

L = 600;

for i = 1:L??%前后延拓的數據

xa(i) = 2*xn(1)-xn(L+2-i);

xz(i) = 2*xn(n0)-xn(n0-i);

end

xnaz = [xa xn xz];%前后延拓

yaz = filtfilt(b,a,xnaz);%做零相位帶通濾波

y = yaz((L+1):(L+n0));??%去延拓

figure(5)

plot(y);

%問題：數據起始點M的取值關系到邊界效應。只有當M取1，401，801，1201……時邊界失真才小，

%取其他值時邊界失真都很大。請問各位其中原因，有何方法使無論起始點取何值都能邊界失真維持

%在較小的范圍內。

%程序本身能夠獨立運行，各位可調整M值看各圖結果。

%謝謝大家了！:handshake :handshake

%延拓是根據武漢大學陳淑珍的一篇參考文獻編寫的，不知如何上傳，但論壇中已有，感興趣的朋友可查看

%論壇中貌似關于零相移濾波器的討論不多，所以好找

%希望能夠得到大家的指點:handshake

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