Linear Systems

Catalog description

Linear Systems provides the foundations of continuous and discrete signal and system analysis and modeling. Topics include a description of continuous linear systems via differential equations, a description of discrete systems via difference equations, input-output relationship of continuous and discrete linear systems, the continuous time convolution integral, the discrete time convolution sum, application of convolution principles to system response calculations, exponential and trigonometric forms of Fourier series and their properties, Fourier transforms including energy spectrum and energy spectral density. Sampling of continuous time signals and the sampling theorem, the Laplace, Z and DTFT. The solution of differential equations and circuit analysis problems using Laplace transforms, transfer functions of physical systems, block diagram algebra and transfer function realization is also covered. A comprehensive study of the z transform and its inverse, which includes system transfer function concepts, system frequency response and its interpretation, and the relationship of the z transform to the Fourier and Laplace transform is also covered. Finally, an introduction to the design of digital filters, which includes filter block diagrams for Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters is introduced.