Question

The Fourier series of an odd periodic function, contains __________

(a) Only odd harmonics

(b) Only even harmonics

(c) Only cosine terms

(d) Only sine terms

The question was posed to me in semester exam.

I would like to ask this question from Common Fourier Transforms in portion Fourier Transform of Signals and Systems

Answer 1

The correct choice is (d) Only sine terms

To elaborate: We know that, for a periodic function, if the dc term i.e. a0 = 0, then it is an odd function. Also, we know that an odd function consists of sine terms only since sine is odd. Hence the Fourier series of an odd periodic function contains only sine terms.