Butterworth模拟低通滤波器论文设计.ppt

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1、Butterworth模拟低通滤波器设计3.利用MATLAB设计BWLP[num,den]=butter(N,wc,'s')确定阶数为N，3-dB截频为wc(radian/s)的Butterworthfilter分子和分母多项式。's'表示模拟域。[N,wc]=buttord(wp,ws,Ap,As,'s')确定模拟Butterworthfilter的阶数N和3-dB截频wc。wc是由阻带参数确定的。's'表示模拟域。[z,p,k]=buttap(N)确定N阶归一化的Butterworthfilter的零点、极点和增益(gain)例：设计满足下列条件的模拟Butter

2、worth低通滤波器fp=1kHz,fs=2kHz,Ap=1dB,As=40dBWp=2*pi*1000;Ws=2*pi*2000;Ap=1;As=40;[N,Wc]=buttord(Wp,Ws,Ap,As,'s');fprintf('Orderofthefilter=%.0f',N)[num,den]=butter(N,Wc,'s');disp('Numeratorpolynomial');fprintf('%.4e',num);disp('Denominatorpolynomial');fprintf('%.4e',den);omega=[WpWs];

3、h=freqs(num,den,omega);fprintf('Ap=%.4f',-20*log10(abs(h(1))));fprintf('As=%.4f',-20*log10(abs(h(2))));omega=[0:200:12000*pi];h=freqs(num,den,omega);gain=20*log10(abs(h));plot(omega/(2*pi),gain);xlabel('FrequencyinHz');ylabel('GainindB');例：设计满足下列条件的模拟Butterworth低通滤波器fp=1kHz,fs=2kHz,

4、Ap=1dB,As=40dBAp=0.62dB,As=40dB050010001500200025003000-80-60-40-200FrequencyinHzGainindBBW型:N=8例：设计满足下列条件的模拟CBI型低通滤波器fp=1kHz,fs=2kHz,Ap=1dB,As=40dB%filterspecificationWp=2*pi*1000;Ws=2*pi*2000;Ap=1;As=40;%Computerfilterorder[N,Wc]=cheb1ord(Wp,Ws,Ap,As,'s');fprintf('Orderofthefilter=%.0

5、f',N)%computefiltercoefficients[num,den]=cheby1(N,Ap,Wc,'s');disp('Numeratorpolynomial');fprintf('%.4e',num);disp('Denominatorpolynomial');fprintf('%.4e',den);例：设计满足下列条件的模拟CBI型低通滤波器fp=1kHz,fs=2kHz,Ap=1dB,As=40dB%ComputeApandAsofdesignedfilteromega=[WpWs];h=freqs(num,den,omega);fpr

6、intf('Ap=%.4f',-20*log10(abs(h(1))));fprintf('As=%.4f',-20*log10(abs(h(2))));例：设计满足下列条件的模拟CBI型低通滤波器fp=1kHz,fs=2kHz,Ap=1dB,As=40dBAp=1.00dB,As=45dB050010001500200025003000-70-60-50-40-30-20-10FrequencyinHzGainindBBW型:N=8CB型:N=5切比雪夫II（CBII）型模拟低通滤波器3.利用MATLAB设计CBIILP[N,wc]=cheb2ord(wp,

7、ws,Ap,As,'s')确定模拟切比雪夫II型滤波器的阶数N。[num,den]=cheby2(N,As,wc,'s')确定阶数为N，阻带衰减为AsdB的切比雪夫II型滤波器的分子和分母多项式。wc由cheb2ord函数确定。*椭圆低通滤波器3.利用MATLAB设计椭圆低通滤波器[N,wc]=ellipord(wp,ws,Ap,As,'s')[num,den]=ellip(N,Ap,As,wc,'s')确定椭圆滤波器的阶数N。wc=wp。确定阶数为N，通带衰减为ApdB，阻带衰减为AsdB的椭圆滤波器的分子和分母多项式。wc是椭圆滤波器的通带截频。