Chapter 17, Problem 30P

a.

To determine

Show that the new coefficient $c_n$ is $\frac{2}{T}{\displaystyle \underset{0}{\overset{\frac{T}{2}}{\int }}f\left(t\right)\cos n{\omega }_{0}tdt}$ for even $f\left(t\right)$ function.

b.

To determine

Show that the new coefficient $c_n$ is $-\frac{j2}{T}{\displaystyle \underset{0}{\overset{\frac{T}{2}}{\int }}f\left(t\right)\sin n{\omega }_{0}tdt}$ for odd $f\left(t\right)$ function.