Page 361 - Schaum's Outline of Theory and Problems of Signals and Systems
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FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS [CHAP. 6
(a) From Eq. (6.27)and usingEq.(1.90), we have
sin [( R - R,) ~/2]
-
- ,j(R-RuXN- I)/Z
sin[(R - R,)/2]
(b) Note from Eq. (6.98) that
we obtain
6.52. Show that if x[n] is real, then its DFT X[k] satisfies the relation
where * denotes the complex conjugate.
From Eq. (6.92)
Hence, if x[n] is real, then x*[n] = x[n] and
6.53. Show that
where * denotes the complex conjugate and
X[k] = DFT{x[n])
We can write Eq. (6.94) as
