A particular periodic waveform with a period of \(10 \mathrm{~ms}\) has the following Fourier coefficients

\[
a_{0}=-5, \quad a_{n}=\frac{16}{n \pi} \sin \frac{n \pi}{4} \cos \frac{n \pi}{4}, \quad b_{n}=\frac{-16}{n \pi} \sin \frac{n \pi}{4} \sin \frac{n \pi}{4}
\]

(a) Write an expression for the terms in the Fourier series up to \(n=8\).

(b) Plot its trigonometric line spectrum

(c) Convert your expression into amplitude and phase form and plot its line spectrum.