Page 226 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 226
CHAP. 51 FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS
(6)
Fig. 5-1 (a) Nonperiodic signal x(r); (b) periodic signal formed by periodic extension of x(r ).
can be rewritten as
Let us define X(w) as
Then from Eq. (5.246) the complex Fourier coefficients c, can be expressed as
Substituting Eq. (5.26) into Eq. (5.231, we have
As To -+ m, o, = 27r/T, becomes infinitesimal (w, - 0). Thus, let w,, = Aw. Then
Eq. (5.27) becomes
