A periodic signal x(t) has a trigonometric Fourier series expansion
$$x\left( t \right) = {a_0} + \sum\limits_{n = 1}^\infty {\left( {{a_n}\,\cos \,n{\omega _0}t + {b_n}\sin \,n{\omega _0}t} \right)} $$
If $$x\left( t \right) = - x\left( { - t} \right) = - x\left( {{{t - \pi } \over {{\omega _0}}}} \right),$$ we can conclude that
A. an are zero for all n and bn are zero for n even
B. an are zero for all n and bn are zero for n odd
C. an are zero for n even and bn are zero for n odd
D. an are zero for n odd and bn are zero for n even
Answer: Option A
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
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