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
(b) Switching Waveform with Duty Cycle d = = 1/3
where fs = 1/T32Fmax
Analog bilateral switch
(c) Resulting PAM Signal (natural sampling, d = T/T, = 1/3)
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