Page 258 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 51 FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS

Hence,
~(t)
ei"~'w X(w - w,)

5-18. Verify the duality property (5.54), that is,

From the inverse Fourier transform definition (5.321, we have

Changing t to - t, we obtain

Now interchanging r and o, we get

Since

we conclude that

5.19. Find the Fourier transform of the rectangular pulse signal x(t) [Fig. 5-16(a)] defined
by

By definition (5.31)

(4 (b)
Fig. 5-16 Rectangular pulse and its Fourier transform.