The fourier series expansion $$$f\left(t\right)\;=\;a_0\;+\;\sum_{n=1}^\infty a_n\cos\;n\omega t\;+\;b_n\sin\;n\omega t$$$ of the periodic signal shown below will contain the following nonzero terms

Let the Laplace transform of a function f(t) which exists for t > 0 be F₁(s) and the Laplace transform of its delayed version f(1 - $$\tau$$) be F₂(s). Let F₁^*(s) be the complex conjugate of F₁(s) with the Laplace variable set as $$s=\sigma\;+\;j\omega$$. If G(s) =$$\frac{F_2\left(s\right).F_1^\ast\left(s\right)}{\left|F_1\left(s\right)\right|^2}$$ , then the inverse Laplace transform of G(s) is