Design a Chebyshev Type 2 bandpass filter of minimum order to meet these specifications.
Passband: 4 kHz to 6 kHz, Gain between 0 dB and ?2 dB
Stopband: <3 kHz and >8 kHz, Attenuation >60 dB
What is the minimum order?
Make a Bode diagram of its magnitude and phase frequency response and check it to be sure the pass and stopband specifications are met.
Make a pole-zero diagram.
What is the time of occurrence of the peak of its impulse response?
The bandwidth in a Chebyshev Type 2 design is determined by the stop bands not the pass bands. For example, in this problem, we set the center frequency to
and the bandwidth to 5 kHz. Then the points at which the attenuation goes above 60 dB are exactly at 3 kHz and 8 kHz and we take whatever we get in the passband. We must experiment with the order to make the passband specification. In this case, the lowest order we can use is 5th order. The impulse response peak occurs at about 0.5 ms.
% Program to design a Chebyshev Type 2 bandpass analog filter
% Passband: 4 kHz to 6 kHz, Gain between 0 and -2 dB
% Stopband: <3 kHz and >8 kHz, Attenuation >60 dB
close all ;
figure('Position',[20,20,1500,800],'PaperPosition',[0.5,0.5,14,14]) ;
N = 5 ; % Filter order
Rs = 60 ; % Minimum stopband attenuation
% Get the zeros and poles and gain of the normalized filter
[z,p,k] = cheb2ap(N,Rs) ;
Hanorm = zpk(z,p,k) ; % Form a normalized system object
[b,a] = tfdata(Hanorm,'v') ; % Get the coefficients
% Center frequency and bandwidth are set by the stop bands not
% the pass band in a Chebyshev Type 2 design
f0 = sqrt(3000*8000) ; % Center frequency in Hz
w0 = 2*pi*f0 ; % Center frequency in radians/s
fbw = 5000 ; % Bandwidth in Hz
wbw = 2*pi*fbw ; % Bandwidth in radians/s
[b,a] = lp2bp(b,a,w0,wbw) ; % Denormalize the filter coefficients
f = [0:10:20000]' ; % Vector of frequencies for graphing (Hz)
w = 2*pi*f ; % Vector of frequencies for graphing (radians/s)
Hafr = freqs(b,a,w) ; % Compute the frequency response
Ha = tf(b,a) ; % Form a denormalized system object
[z,p,k] = zpkdata(Ha,'v') ; % Get the pole and zero locations
[ha,t] = impulse(Ha) ; % Get the impulse response
% Graph all results
subplot(2,2,1) ;
ptr = semilogx(f,20*log10(abs(Hafr)),'k') ; set(ptr,'LineWidth',2) ;
grid on ;
xlabel('Frequency, {\itf} (Hz)','FontName','Times','FontSize',24) ;
ylabel('|H_{\ita}({\itj}2\pi {\itf} )|_{dB}','FontName','Times','FontSize',24) ;
title('Frequency Response','FontName','Times','FontSize',36) ;
set(gca,'FontName','Times','FontSize',18) ;
subplot(2,2,3) ;
ptr = semilogx(f,angle(Hafr),'k') ; set(ptr,'LineWidth',2) ;
grid on ;
xlabel('Frequency, {\itf} (Hz)','FontName','Times','FontSize',24) ;
ylabel('Phase of H__{\ita} ({\itj}2\pi {\itf} )','FontName','Times','FontSize',24) ;
set(gca,'FontName','Times','FontSize',18) ;
subplot(1,2,2) ;
ptr = pzplot(z,p) ;
print -depsc -adobecset 'temp1' ;
figure('Position',[40,40,1500,800]) ;
ptr = plot(t*1000,h,'k') ; set(ptr,'LineWidth',2) ; grid on ;
xlabel('Time, {\itt} (ms)','FontName','Times','FontSize',24) ;
ylabel('h({\itt})','FontName','Times','FontSize',24) ;
title('Impulse Response','FontName','Times','FontSize',36) ;
set(gca,'FontName','Times','FontSize',18) ;
You might also like to view...
In what ways does the development of the railroad industry in the late 19th century illustrate the limitations of the myth of individual free enterprise in American history? What did government hope to attain by its promotion of railroad construction? What, in fact, did it attain?
What will be an ideal response?
The hydrangea is an example of a shrub that needs annual pruning
Indicate whether the statement is true or false
During the last two weeks, a technician who is married with no children earned $2154 in commissions. How much was withheld from the technician's paycheck for Medicare?
Fill in the blank(s) with the appropriate word(s).
Which statement about TDM is true?
A) TDM uses time slots to carry signals instead of frequencies and multiplexes digital signals into the time slots, not analog signals, as with FDM. B) TDM is the most widely used transport protocol in the world-wide communications network. C) TDM rides on all types of media, copper, radio frequencies, and fiber. D) There are two distinct steps in the TDM process, conversion and multiplexing. E) All of the above.