Question

How can we define the coefficients half wave symmetry when n is even?

(a) an=0 and bn=0 and a0=0

(b) an=4/T∫x(t)cos(nwt)dt  and bn=0= a0

(c) an=4/T∫x(t)sin(nwt)dt and bn=4/T∫x(t)cos(nwt)dt and a0=0

(d) an=4/T∫x(t)sin(nwt)dt and bn=4/T and a0=0

This question was posed to me in a dream while sleeping

Question is taken from Symmetry Properties of the Fourier Series in section Fourier Series of Signals and Systems

Answer 1

The correct option is (a) an=0 and bn=0 and a0=0

The best I can explain: If it is half wave symmetry then we define the fourier coefficients as-

an=0 and bn=0 and a0=0 if n is an even number.