Question

1. Express the following signals in their trigonometric, polar and compact exponential forms. if it is necessary to expand the signals and indicate the fundamental frequency $\omega_{0}$ of them.

Answer 1

e) x(t) = cos² t

= 1 + cos 2t / 2

=

x(t) = cos^2 t = 1 + cos 2t/2 = 1/2 (1 + cos 2t) = 1/2 (1 + e^2it - e^-2it/2) x(t) = sin^2 t = 1 - cos 2t/2 = 1/2 (1 - cos 2t) = 1/2 (1 - e^2it + e^it/2) x(t) = cos^3t = cos 3t - 3 cost/4 x(t) = sin^3t = 3 sint -sin 3t/4

=

f) x(t) = sin² t

= 1 - cos 2t / 2

=

=  

g) x(t) = cos³t

= cos 3t - 3cost / 4

h) x(t) = sin³t

= 3sint -sin 3t / 4