Page 267 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS [CHAP. 5

By the time-shifting property (5.50)

Thus, we have

5.32. Using the time convolution theorem (5.58), find the inverse Fourier transform of
X(w) = l/(a + j~)~.

From Eq. (5.45) we have

Now

Thus, by the time convolution theorem (5.58) we have

x(r) = e-"u(r) * e-"u(t)

Hence,

5.33. Verify the integration property (5.57), that is,

From Eq. (2.60) we have