problem of fourier series

[bhuvaneshnick]

Choose the function f(t) ; −∞ < < +∞, for which a Fourier series cannot be defined.
(a) 3 sin(25t) (b) 4 cos(20t + 3) + 2 sin (10t)
(c) e-|t| sin(25t) (d) 1

fourier series are available for all periodic signal .its obvious that all the four are periodic.But somewhere i hear that fourier series is not possible for constant .could someone give me hint for the answer ,so try to come up. Thank you

 

[Tony Stewart]

c) is not periodic function

 

[bhuvaneshnick]

3 sin(25t)------period is 2pi/25

cos(20t + 3) + 2 sin (10t)----T1=2pi/20 and T2=2pi/10


e-|t| sin(25t)----T1=2pi and T2 =2pi/25 and the ratio of T1 and T2 fives rational number .so its periodic

1---periodic with period infinity

 

[Tony Stewart]

The exponent for t<0 is not periodic

 

[bhuvaneshnick]

okay got you

but looks the constant function .its not function of t and its period is undefined ,doesnt it look doubt full that it may be non periodic ?