Another definition of bandwidth for a signal is the 90% energy containment bandwidth. For a signal with

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Another definition of bandwidth for a signal is the 90% energy containment bandwidth. For a signal with energy spectral density G(f) = |X(f)|2, it is given by B90in the relation B90 · B90 G(f)df = 2 / G(f)df; 0.9ETotal – B90 00 | G(f) df = 2 G(f)df ETotal %D -00

Obtain B90 for the following signals if it is defined. If it is not defined for a particular signal, state why it is not. 

(a) x(t)  = e-at u(t), where α is a positive constant

(b) x2 (t) = 2W sinc (2W t) where W is a positive constant 

(c) x3 (t) = II (t/Ï„) (requires numerical integration)
(d) x4 (t) = Λ (t/τ) (requires numerical integration)

(e) x5 (t) = e-a|t|

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