Question

If a periodic function f(t) of period T satisfies f(t) = −f (t + T/2) , then in its Fourier series expansion

(a) The constant term will be zero

(b) There will be no cosine terms

(c) There will be no sine terms

(d) There will be no even harmonics

The question was asked during an online exam.

My query is from The z- and s-Domain Relationship topic in chapter Digital Control Systems of Control Systems

Answer 1

Right option is (b) There will be no cosine terms

For explanation I would say: The fourier series will contain the cosine terms if the periodic function f (t) of period T satisfies f (t) = -f(t+T/2), and this can be proved by the basic definition of the fourier transform.