Signals and Systems Theory

Course Outline

• Introduction to signal and systems theory
• Continuous and Discrete time linear systems, Impulse response, Linear Time Invariant (LTI) systems, lineal convolution
• Fourier series, and the family of complex exponentials signals, the complex  exponential signals as eigensignals of LTI systems, Continuous and Discrete time Fourier Transform, Cosine and Sine transform, Frequency response, LTI systems as solvers of ordinary differential equations 
• Distribution functions, regular and singular distribution functions, generalized Fourier transform 
• Laplace Transform, Z-transform, Transfer function, BIBO stability of Continuous and Discrete time LTI systems
• State space, States, State equations, Controllability, Observability, Asymptotic stability, Stabilization of unstable systems,  State feedback
• Partial Differential Equations and their solution by separation of variables