schaum's outline of signals and systems

CHAP. 51

FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS

Hence, ~ ( t e)i " ~ ' wX(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.