2.7 a. The root mean-square (rms) bandwidth of a low-pass signal g(t) of finite energy is defined by .2יר rms where |G(f)P is the energy spectral density of the signal. Correspondingly, the root mean-square (rms) duration of the signal is defined by T. rms Using these definitions, show that Tm, W. rms rms Assume that g(t)|→ 0 faster than 1/ as |r| → 0. b. Consider a Gaussian pulse defined by 8(1) = exp(-n) Show that for this signal the equality Tm W, is satisfied. Hint: Use Schwarz's inequality in which we set 81(1) = tg(t) and dg(t) 82(1) = dt %3D -15

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.