Fourier Transforms

Fourier Integrals and Fourier Transforms Exercise 1 : Fourier Series For the following periodic function: $$ f(t) = \begin{cases} -1 & \text{for } -\frac{T}{2} \leq t < 0 \\ 1 & \text{for } 0 < t \leq \frac{T}{2} \end{cases} $$ Calculate the Fourier series for $$ f(t) = \begin{cases} 0 & \text{for } -\frac{T}{2} \leq t < -\frac{t_0}{2} \\ -1 & \text{for } -\frac{t_0}{2} \leq t < 0 \\ 1 & \text{for } 0 < t \leq \frac{t_0}{2} \\ 0 & \text{for } \frac{t_0}{2} < t \leq \frac{T}{2} \end{cases} $$Exercise 2 : Limiting Spectrum (T \to \infty) Now perform the limiting process for $T \to \infty$ and obtain the amplitude spectrum. ...