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低通滤波器的设计
设计低通滤波器的要求：
设低通滤波器通带截止频率为ωp=0.2π，阻带截止频率为ωs=0.4π，通带波纹Ag=0.5dB，最小阻带衰减Ar=50dB。
wp=0.2*pi;wr=0.4*pi;
trwidth=wr-wp; %过渡带宽度
N=ceil(6.64*pi/trwidth)+1; %滤波器的长度
n=0:1:N-1;
wc=(wr+wp)/2;
hd=ideal_lp(wc,N);
w_ham=(hamming(N))’;
h=hd.*w_ham;
[db,mag,pha,grd,w]=freqz_m(h,[1]);
delta_w=2*pi/1000;
Ap=-(min(db(1:1:wp/delta_w+1)));
Ar=-round(max(db(wr/delta_w+1:1:501)));
subplot(221);stem(n,hd);title(‘理想单位脉冲响应hd(n)’)
subplot(222);plot(n,w_ham);title(‘海明窗w(n)’)
subplot(223);stem(n,h);title(‘实际单位脉冲响应h(n)’)
subplot(224);plot(w/pi,db);title(‘幅度响应(dB)’)
子程序：(1)function hd=ideal_lp(~,~)
%Ideal Lowpass filter computation
%[hd]=ideal_lp(wc,N)
% hd=ideal impulse response between 0 to N-1
% wc=cutoff frequency in radians
% N=length of the ideal filter
%
wp=0.2*pi;wr=0.4*pi;
tr_width=wr-wp;
N=ceil(6.64*pi/tr_width)+1; wc=(wr+wp)/2;
alpha=(N-1)/2;
n=0:1:(N-1);
m=n-alpha+eps;
hd=sin(wc*m)./(pi*m);
(2)function [db,mag,pha,grd,w] = freqz_m(~,~)
% Modified version of freqz subroutine
% ————————————
% [db,mag,pha,grd,w] = freqz_m(h,[1]);
% db = Relative magnitude in dB computed over 0 to pi radians
% mag = absolute magnitude computed over 0 to pi radians
% pha = Phase response in radians over 0 to pi radians
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