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5.77. The sampling theorem in the frequency domain states that if a real signal x( t ) is a duration­ limited signal, that is,
x( t ) = 0

then its Fourier transform X( w ) can be uniquely determined from its values X( nrr / tM) at a series of equidistant points spaced rr/ tM apart. In fact, X( w) is given by
;, ( nrr ) sin( w t M – nrr )
X ( w ) = X –
n = -oo IM w tM – nrr
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.

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