Find exponential series for the signal shown in figure,

Solution:

$ T=1, \Omega_0=\frac{2 \pi}{T}=\frac{2 \pi}{1}=2 \pi\\ $

Consider the equation of a straight line,

$ \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}\\ $

On substituting the coordinates of points P and Q in eq,

$ \frac{x(t)-0}{1-0}=\frac{t-0}{1-0} \Rightarrow x(t)=t\\ $

$ c_0=\frac{1}{T} \int_0^T x(t) d t=\frac{1}{1} \int_0^1(t) d t=\left[\frac{t^2}{2}\right]_0^1=\frac{1}{2}\\ $

$ \begin{gathered} c_n=\frac{1}{T} \int_0^T x(t) e^{-j …