Answer Happy

A continuous-time periodic signal is given as follows: ta(t) = 16 sin(2x fit) + 8 cos (26 f2t), where fi = 1500 Hz, and f2 = 2000 Hz. (a) Draw the line spectrum of xa(t). (b) Determine the average power of each freq. component. Hence, calculate the total average power. (C) Show that xa(t) is periodic with a period of 2 ms. Hence, plot 4 periods of the signal for verification (a) Determine framp(min) the minimum sampling frequency needed to sample wa(t), hence use 1.2 of such value. (e) Specify the anti-aliasing and reconstruction analog filters specifications needed if an atten- uation of 0.1 dB in the passband ( ap = 0.1 dB) is required and an attenuation of 40 dB in the stop-band ( ag 40 dB) is required. Hint: Just find the order of the filter N and write the numerator and denominator coefficient vectors. (f) Find and plot x(n), the sampled version of caſt). (g) Describe how to used a(n) and an appropriate window to display the spectrum of the orig- inal continuous-time signal Ba(t) such that all its frequency components are well resolved. Plot the magnitude spectrum for verification. Also, determine the minimum duration needed in seconds. Finally, show the block diagram of the system.