The Fourier coefficients of a periodic input signal are: [ a_{0}=0 quad a_{n}=0 quad b_{n}=frac{8 V_{mathrm{A}}}{(n pi)^{2}}

Question:

The Fourier coefficients of a periodic input signal are:

\[
a_{0}=0 \quad a_{n}=0 \quad b_{n}=\frac{8 V_{\mathrm{A}}}{(n \pi)^{2}} \sin \left(\frac{n \pi}{2}ight)
\]

The signal has \(V_{\mathrm{A}}=10 \mathrm{~V}\) and \(T_{\mathrm{O}}=20 \pi \mathrm{ms}\) and drives a circuit with a transfer function of

\[
T(s)=\frac{s}{s+100}
\]

Find the amplitude of the first four nonzero terms in the Fourier series of the steady-state output. construct plots of the amplitude and phase spectra for the input and output waveforms and comment on any differences.