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3) A signal x(/) = 2cos(24) ,where f =1A-Hz is sampled at time instants r = nr„n =0,±1,±2 where the sampling rate f, = 4IdIz and the duty cycle d =0.5. Assume that the natural sampling is used. (a) Sketch the sampled signal for 0 s r 587; . (b) An ideal low-pass filter with gain 1/d is used to recover x(/) from the sampled signal. Find the filter output (i.e., the recovered signal) and compare it with the original signal. (c) Repeat (a) and (b) when the flat-top sampling is used with the same duty cycle. Is the filter output the same as in (b)? Why? Natural Sampling (Gating) (a) Baseband Analog Waveform The sampled (PAM) signal is x(t) t - = II T k=-00 s (i) (b) Switching Waveform with Duty Cycle d = = 1/3 T where fs = 1/T32Fmax Analog bilateral switch Ts T Xs (t) s(1) Clock Is (c) Resulting PAM Signal (natural sampling, d = T/T, = 1/3)

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