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(3) Consider the following continuous-time signal 1 (t) = Ial(t) +1,2(t) +123(t), please turn the page over 2 where Tal(t) 142(t) Tag(t) 2 sin(2xfit) + cos(2 fot), 4 sin(2x f3t) cos(2xfat), 5 cos(27fst) cos(2 fot), f1 = 1 kHz, f2 -13.5 kHz, f3 = 7.5 kHz, fa = 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 1,2(t) and 1,3(t), 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 stopband Qs = 40 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?