Page 304 - Schaum's Outline of Theory and Problems of Signals and Systems
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CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS
63 THE FOURIER TRANSFORM
A. From Discrete Fourier Series to Fourier Transform:
Let x[n] be a nonperiodic sequence of finite duration. That is, for some positive
integer N,,
Such a sequence is shown in Fig. 6-l(a). Let x,Jn] be a periodic sequence formed by
repeating x[n] with fundamental period No as shown in Fig. 6-l(b). If we let No -, m, we
have
lim xNo[n] = x[n]
No+-
The discrete Fourier series of xNo[n] is given by
where
(4
Fig. 6-1 (a) Nonperiodic finite sequence x[n]; (6) periodic sequence formed by periodic extension of
xhl.
