Question

S. If the signal x() defined for -o0 <I c by x()-sine (0.5)sinc(20) is flat top sampled, a) what is the minimum sampling rate necessary in order to avoid aliasing? b) What is the maximum duration that the flat top pulses can have if the sampled signal meets the minimum sampling requirements specified in part a)? (20 pts.)

Answer 1

X (t) = sinc^2 (0 . 5 t) sinc (2 t) concept: - Min^m sampling Rate required in order to avoid Aleasing is equal to Nyquist Rate Nyquist Rate (N R) 2 f m = f sampling Where fm is the frequency of Band - Limited message signal for No Ariasing effect fs lesserthan 2 fm (fs) min^m = 2 fm concept 2 sinc (t) Fourier transform General form of sin ct = sin c (2 nft) Concept 3 sin c (0 . 5 t) times sin c (0 . 5 t) times sin (2 t) rightarrow Multiplication in time domain is convolution in frequency domain sin c (0 . 5 t) F. t 1/0 . 5 (f/0 ./ 5) sin (2 t) rightarrow 1/2 rect (f/2) sin c (0 . 5 t) = sin (0 . 5 pi t)/0 . 5 pi t comparing with standard form sin (2 pi f m t)/2 pi f m t) 2 pi f m_1 = 0 . 5 pi fm