Orthogonal expansions of signals. Periodic signals: Fourier series. Properties of Fourier series. Parseval's theorem. Non-periodic signals: continuous-time Fourier transform. Properties of the Fourier transform. Basic Fourier transform pairs.
Representation of signals in terms of impulses. The unit impulse response. The convolution integral. Properties of the convolution. Methods for calculating convolutions. Convolution of periodic signals. Causality, stability and invertibility of continuous-time LTI systems. Characterization of LTI systems: time and frequency domains.
The Laplace transform: definition and properties. Region of convergence for Laplace transforms. The inverse Laplace transform. Transfer function of a LTI system. Analysis and characterization of LTI systems using the Laplace transform. LTI systems described by differential equations.