Question

When does a wave posses a quarter wave symmetry?

(a) It has either even or odd symmetry

(b) It has half wave symmetry

(c) even/odd symmetry and half wave symmetry

(d) It is even in one quarter and odd in the other

This question was addressed to me by my school teacher while I was bunking the class.

My question is based upon Symmetry Properties of the Fourier Series in chapter Fourier Series of Signals and Systems

Answer 1

Correct option is (c) even/odd symmetry and half wave symmetry

To explain: A signal is said to posses quarter wave symmetry when it is either odd or even symmetry and has half wave symmetry. These signals are shifted to left or right by T/4 with a half wave symmetry but the even symmetry of the original unshifted towards the odd symmetry it is said to be quarter wave symmetry.