Question

The odd part of a signal x(t) is?

(a) x(t)+x(-t)

(b) x(t)-x(-t)

(c) (1/2)*(x(t)+x(-t))

(d) (1/2)*(x(t)-x(-t))

This question was posed to me in an interview for internship.

My question comes from Discrete Time Signals topic in division Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

The correct answer is (d) (1/2)*(x(t)-x(-t))

To elaborate: Let x(t)=xe(t)+xo(t)

=>x(-t)=xe(-t)-xo(-t)

By subtracting the above two equations, we get

xo(t)=(1/2)*(x(t)-x(-t)).