§ 14-1 Trigonometric Fourier series
Any periodic waveform f(t)=f(t+T) can be expressed
by a Fourier series provided that
(2) It has a finite average value over the period T;
(3) It has a finite number of positive and negative
maximums in the period T.
(1) If it is discontinuous,there are
only a finite number of discontinuous in
the period T;
Example,Find the Fourier series
)20(210)( ???? ??? tttf
521020 ??a
)(c o s)210(1 20 ttdnta n ????? ???
)(s i n)210(1 20 ttdntb n ????? ???
? ? ???
? nn
1002co s2
2
10
2 ?????
?ttttf ?????? 3s i n3102s i n210s i n105)( ?????
t?
?2 ?4
)(tf
10
0
0c os1s i n2101
2
0
2 ???
?
??
? ?? ????
?? tnntnn
t
?
?????
2
0
2 s i n
1c os
2
101
??
?
??
? ??? tn
n
tnn t
?
?
?
??
1
s i n105
n n
tn ?
?