Please Show All the Steps Carefully. Show both Written approach and Matlab appro

Question

Please Show All the Steps Carefully. Show both Written approach and Matlab approach. Highest rating will be given to those who show all the Written and Matlab approaches clearly and with proper explanation.

It is desired to design a two pole low pass filter that has a peak magnitude response at ?-0 and a 3dB bandwidth at S-n4. Find the frequency response of this filter and use Matlab to sketch the magnitude and the phase response (make sure the specifications are met. Implement the filter in a canonical form and in a cascade form

Explanation / Answer

b0 = 1.55451;
b1 = [1 1];
b2 = [1 -1.066 1];
a1 = [1 -0.63];
a2 = [1 -1.4461 0.7957];

b = b0*con(b1,b2);
a = co(a1,a2);

[h,w] = freqb,a,'whole',2001);
plot(w/pi,*log10(abs(h)))
ax = ga;
ax.Ym = [-100 20];
ax.ick = 0:.5:2;
xlal('Normalized Frequency ( imespi rad/sample)')
ylal('Magnitude (dB)')

h = fres(b,a,w);
mag = abs(h);
phe = agle(h);
phadeg = pha*180/pi;

splot(2,1,1), loglog(w,mag), grid on
xlabel 'Freq (rad/s)', ylabel Magnitude
subot(2,1), sem(w,phasedeg), gr on
xlael 'Frequency (rad/s)', ylal 'Phase (degrees)'
end

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