Signals (definitions, signal categories, multi-dimensional signals, discrete time signals, continuous time signals, deterministic and stochastic signals, duration, causality, energy and power, periodicity, symmetry, signals operations, linear convolution, correlation, discrete time random signals, two-dimensional signals) Continuous Time Fourier Transform – CTFT (definition, pairs, properties, CTFT of power signals, CTFT computation, meaning of CTFT). Discrete Time Fourier Transform – DTFT (definition, pairs, properties, DTFT computation, convolution via DTFT, DTFT of autocorrelation). Laplace Transform (one-sided Laplace Transform, pairs, region of convergence, properties, initial value theorem, final value theorem, inverse Laplace Transform, double-sided Laplace Transform). z-Transform (double-sided z-Transform, region of convergence, pairs, properties, z-Transform computation, poles and zeros, convolution via z-Transform, inverse z-Transform, signal stability). Systems (definitions, properties, LTI systems, LTI systems properties). Continuous Time LTI Systems (description using differential equations, frequency response via CTFT, transfer function via Laplace Transform, system stability). Discrete Time LTI Systems (description using difference equations, FIR, IIR, solution of difference equations, frequency response via DTFT, transfer function via z-Transform, feedback system).
The objective of this course is to familiarize students with the concepts of signals and systems, and to provide theoretical and practical knowledge on methods and tools used for developing signal processing systems. The course has both theoretical and practical aspects. The students have the opportunity to learn how to implement the theoretical notions to which they are introduced, and many examples with the use of system modelling / programming languages, such as MATLAB.
Upon successful completion of this course, students should be able to: