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(2) Consider the following continuous-time signal fa(t) = Hai(t) +1.2(t) + X(t), please turn the page over 1 where Tar(t) = 2 sin(2xf1t) + cos(2/2), 1.2() 4 sin(2/3t) cos(2xfat), 13(t) = 5 cos(2fst) cos(2*fet). f1 = 1 kHz, 12 = 13.5 kHz, S3 = 7.5 kHz, f4 = 10 kHz, fs = 2.5 kHz, and fo = 10 kHz. It is required to design a digital signal processing-based system to separated the two signals ta(t) and 193(e), where the system have one input and 2 outputs. (a) Draw the line spectrum of the signals using different colors to distinguish them from each others. (b) Determine the minimum number of filters and types needed to achieve the above goal. (c) Find the minimum required sampling rate framp. Hence, sketch the overall block diagram of the system. (d) Assume the digital filters order is 8 and that the attenuation in the passband a, = 0.1 dB. (e) For each filter, specify the requirements, hence design and write the difference equations of the digital filters needed. (1) What are the amplitudes of the filter outputs for the different frequency in their passband?