Analog & Digital Filtering, Electrical Engineering

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1) Assume that we are given the continuous-time signal
xa (t) = xa1 (t) + xa2 (t) + xa3 (t),
where,
xa1 (t) = 2 + cos3 (2pf1 t + p
3 ) + 2 cos(2pf2 t),
xa2 (t) = 2 cos(2pf3 t) cos(2pf4 t),
xa3 (t) = 5 cos(2pf5 t) + 2 cos(2pf6 t),
f1 = 5 Hz, f2 = 12 Hz, f3 = 5 Hz, and f4 = 35 Hz, f5 = 60 Hz, and f6 = 100 Hz. It is required
to design a digital signal processing-based system to separated the signals xa1 (t) and xa2 (t)
from the signal xa (t). Assuming a sampling frequency of 200 samples/second, the order of the
?lters to be n = 6, and an attenuation not more that 1 dB in the passband for the used digital
?lters.

(a) Determine the requirements of the digital ?lters needed.
(b) Design and write the di?erence equations for the digital ?lters. Check for stability.
(c) Plot the attenuation (in dB) response of each ?lter to verify your design.
(d) Draw the complete block diagram of the system giving the requirements of the other com-
ponents of the system needed in conjunction with the digital ?lters.

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