Show me how to calculate the following pass wand with for different length L=10,

Question

Show me how to calculate the following pass wand with for different length L=10,10 and 40

Show me the code and step by step process to find the differerent PBWs with the corresponding L's. The answers are in the table bellow to double check answer.

first=0;

last=19;

nn=first:last;

L=20;     % or 40

bb=(2/L).*cos(0.44*pi*nn);     % bandpass filter at ww=0.44*pi

ww=-pi:(pi/500):pi;

HH_bb=freqz(bb,1,ww);

plot(ww,abs(HH_bb))

xlabel('frequency(radians)')

ylabel('a bandpass filter ')

title('a frequency component at 0.44pi')

jkl=find(abs(HH_bb)>=( max(abs(HH_bb))*0.707)); % L=10

zz=HH_bb(jkl);  % store the values that are higher than 0.707*1.0971

PBW=(length(zz)/2)*2/1000  

Pass Band Width for various L 10 20 40 0.1 62pi 0.088pi 0.042 pi Pass Band Width *We can see that the filter length "L' is inversely relates with the pass-band width.

Explanation / Answer

MATLAB CODE:

first=0;
last=19;
nn=first:last;
L=20; % or 40
bb=(2/L).*cos(0.44*pi*nn); % bandpass filter at ww=0.44*pi
ww=-pi:(pi/1000):pi;
HH_bb=freqz(bb,1,ww);
plot(ww,abs(HH_bb))
xlabel('frequency(radians)')
ylabel('a bandpass filter ')
title('a frequency component at 0.44pi')
jkl=find(abs(HH_bb)>=( max(abs(HH_bb))*0.707)); % L=10
%zz=HH_bb(jkl); % store the values that are higher than 0.707*1.0971
%PBW=(length(zz)/2)*2/1000;

w_upper=jkl((length(jkl)/2)+1:end); % stores positive bandwidth

w_L=ww(w_upper(1)); % picks lower frequency point of w_upper to corresponding value of frequency in ww
w_H=ww(w_upper(end)+1); % picks higher frequency point of w_upper plus 1 to corresponding value of frequency in ww
PBW=w_H-w_L;

NOTE : I just added some lines to your code.

w_upper stores only the points of positive bandwidth

w_L is the exact frequency value of ww corresponding to first value of w_upper

w_H is the exact frequency value of ww corresponding to last value i.e. higher frequency point of w_upper.

Here 1 is added to w_upper(end) because we are indulged in calculation of indices

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