Question

3. (I0pts) An elliptic analog bandpass filter is to be designed with the following specifications: passband edge: 30 kHz and 50 kHz stopband edge: 25 kHz and 55 kHz peak passband ripple: 0.25dB minimum stopband attenuation: 40dB What's the bandedge of the corresponding elliptic analog low-pass filter? (Note: There are two possible solutions but you only have to provide one) (5pts) What's the filter order of the corresponding elliptic analog low-pass filter? (You can use Matlab to get your answer. However, you need to include your code to receive full credit) (5pts)

Answer 1

the solution :-

the bandedge of the coresponding elliptics

The band edge and filter order of LPF are same as taht of high pass filter:

For LPF:

%Specifications
Rp=0.25;Rs=40;
Fs=44000;%Assumption
fp=6000;fs=4000;
wp=2*fp/Fs;ws=2*fs/Fs;
[N1,wc]=buttord(wp,ws,Rp,Rs)
[b1,a1]=butter(N1,wc);
[H1,f]=freqz(b1,a1,1024,Fs);
tf1=tf(b1,a1)
%Frequency response
figure(1)
subplot(211)
plot(f,20*log(abs(H1)),'r')
xlabel('f')
ylabel('|H(f)| in db')
title('Log magnitude response-butterworth')
subplot(212)
plot(f,angle(H1),'g')
xlabel('f in Hz')
ylabel('<H(f)>')
title('Phase response-butterworth')

Log magnitude response-butterworth 200 o 200 S 400 S -600 800 1000 -1200 5000 10000 15000 20000 25000 Phase response-butterworth 4 2 2 5000 10000 15000 20000 25000 f in Hz

COmmand window:

Butterworth Low pass filter
N1 = 14
wc = 0.24925

the bandedge of elliptics lpf

______________________________________________________________________-

Band edge of elliptic LPF:

disp('Elliptic Low pass Filter with the lowest edge of BPF')
%Specifications
Rp=0.25;Rs=40;
fp=[30000];fs=[25000];
Fs=2*(10^5)
wp=2*fp/Fs;ws=2*fs/Fs;
[N2,wp] = ellipord(wp,ws,Rp,Rs)
[b2,a2] = ellip(N2,Rp,Rs,wp);
[H2,f]=freqz(b2,a2,1024,Fs);
tf2=tf(b2,a2)
%Frequency response
figure(1)
subplot(211)
plot(f,20*log10(abs(H2)),'r')
xlabel('f in Hz')
ylabel('|H(f)| in db')
title('Log magnitude response-elliptic')
subplot(212)
plot(f,angle(H2),'g')
xlabel('f in Hz')
ylabel('<H(f)>')
title('Phase response-elliptic ')

Log magnitude response-elliptic 20 -40 r -60 80 -100 20000 40000 60000 80000 f in Hz Phase response-elliptic 4 2 -2 40000 20000 60000 80000 100000 f in Hz

Command window:

Elliptic Low pass Filter with the lowest edge of BPF
Fs = 200000
N2 = 6
wp = 0.30000

therefore ...............the answers was given and sloved