In natural sampling (or switching), an analog signal x(t) of bandwidth W is multiplied by a periodic train of rectangular pulses c(t).
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# <ol><li>In natural sampling (or switching), an analog signal x(t) of bandwidth W is multiplied by a

periodic train of rectangular pulses c(t). Given that the fundamental frequency of this periodic train is fs, and that the duration of each pulse is τ (with fsτ &lt; 1), do the following: </li><li>(a) Find the amplitude spectrum |Xs(f)| of the signal xs(t) = x(t)c(t). Assume that fsτ = 0.2 and sketch in the range |f| ≤ 5fs + W. You may use any amplitude spectral shape for X(f) in your sketch. </li><li>(b) Show that the original signal x(t) can be recovered from x(t), provided that the conditions of the sampling theorem are satisfied. </li></ol>

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