Page 300 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 51 FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS 287

then its Fourier transform X(w) can be uniquely determined from its values X(nsr/t,) at a
series of equidistant points spaced n/t, apart. In fact, X(w) is given by

ot, - n.rr
n= -00
Verify the above sampling theorem in the frequency domain.
Hint: Expand x(t) in a complex Fourier series and proceed in a manner similar to that for
Prob. 5.59.