Question

Determine the Fourier series representation of

Let \(\left.x_{(} t\right)=\left\{\begin{array}{rr}t, & 0 \leq t \leq 1 \\ -t, & -1 \leq t \leq 0\end{array}\right.\), be a periodic signal with fundamental period of \(T=2\) and Fourier series coefficients \(a_{k}\).

a) Sketch the waveform of \(x(t)\) and \(\frac{d x(t)}{d t}\) 

b) Calculate \(a_{0}\) 

c) Determine the Fourier series representation of \(g(t)=\frac{d x(t)}{d t}

d) Using the results from Part (c) and the property of continuous-time Fourier series to determine the Fourier series coefficients of \(x(t)\)


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