\displaystyle \mathcal{L} [f(t)] = \int_{0}^{T}{e^{-s\tau} f(\tau) \ d\tau} + e^{-sT} \int_{0}^{T}{e^{-s\tau} f(\tau+T) \ d\tau} +  e^{-2sT} \int_{0}^{T}{e^{-s\tau} f(\tau+2T) \ d\tau} + 