A sinusoidal signal is produced from a programmable digital signal generator by filtering the staircase approximation to a sine signal, as demonstrated below wherein $A$ is any finite constant and $T$ is the fundamental period.

a$)$ Calculate the coefficients of complex exponential Fourier series expansion of the periodic signal $x(t)$ in terms of $A,k($number of harmonics$),$ and $.$

b$)$ Demonstrate that the even harmonics are zero.

c$)$ Express $x(t)$ as a complex exponential Fourier series.

d$)$ Determine the trigonometric Fourier series representation of $x(t).$

e$)$ Plot the complex exponential Fourier series representation found in part $($c$)$ for $300$ harmonics. $($You can sketch in MATLAB, MATHEMATICA, or any other appropriate computer program you wish!$)$