Problem 6

Consider the frequency multiplier system below. Given a sinusoidal input, the nonlinear sub-system generates a periodic output, y(t) with the same fundamental frequency (f) as the input.The Fourier series coefficients of y(t) are known to be:

C_{n}=\left\{\begin{array}{c}

\frac{1}{\pi\left(1+n^{2}\right)}, \text { when } n \text { is odd } \\

0, \text { Else }

\end{array}\right. Y(f)=\sum_{-\infty}^{\infty} C_{n} \delta\left(f-n f_{0}\right), z(t)=2 C_{n} \cos \left(2 \pi n f_{0} t\right)