Find even and odd component of the signal x(t)=(1+t^3) cos(10t).

 Find even and odd component of the signal x(t)=(1+t³) cos(10t).

Given,

x(t)=(1+t³) cos(10t)

x(-t)=(1-t³) cos(10t)

Even component=(x(t)+x(-t))/2

                                 =( (1+t³) cos(10t) + (1-t³) cos(10t))/2

                                 =(cos(10t)+ t³cos(10t)+ cos(10t)-t³cos(10t))/2

                                 =cos(10t)

Odd component=(x(t)-x(-t))/2

                               =( (1+t³) cos(10t) - (1-t³) cos(10t))/2

                               =t³cos(10t)