Page 290 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 51 FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS

Fig. 5-33

and

which indicates the inverse relationship between bandwidth and risetime.

5.57. Another definition of bandwidth for a signal x(t) is the 90 percent energy containment
bandwidth W,, defined by

where Ex is the normalized energy content of signal x(t). Find the W, for the
following signals:
(a) x(t) = e-"'u(t), a > 0
sin at
(b) x(t) = -
rr l
(a) From Eq. (5.155)
1
~(t) e-"u(t) - X( W) = -
=
a +jo
From Eq. (1.14)

Now, by Eq. (5.180)