Part 2
a
b.
When both the system 1 and system 2 have the same inputs the outputs would not be equal. This is defined by the following codes;
Therefore the outputs are different even if the inputs are similar.
c.
d.
Y1
= filter(b1,a1,x)
Y2 = filter(b2,a2,x)
xw=fft(x);
Y1w=fft(Y1)
Y2w=fft(Y2);
figure(3)
stem(abs(xw));
figure(4)
As seen from the above two graphs from the MATLAB the two signals are the same therefore both looks like the input signal.
e.
xw=fft(x);
Y1w=fft(Y1)
Y2w=fft(Y2);
stem(abs(Y1w));
figure(5)
stem(abs(Y2w));
From the above three Fourier transform magnitude, the three magnitudes of the Fourier are the same.
f.
y22=[-3 1];
y23=[1 -3];
y24=[3 2];
Each of the all pass filter have the same effect, the will allow frequency from 15Hz to pass. Actually, these are not ideal all pass filter since there are some slight frequencies which are inhibited from passing but that is negligible.
g.
For the first one decreases from maximum positive value to the negative value then stabilizes around zero value. While for the second energy graph it decays from maximum positive value and moves to zero then increases to some positive value less than 0.5 then settle at zero.
References
KUMAR, A., 2012. SIGNALS AND SYSTEMS. 2nd ed. Liverpool: PHI Learning Pvt. Ltd.
Oppenheim, A., 2013. Signals and Systems. 3rd ed. Chicago: Pearson Education Limited.
