Theory and applications of mathematical methods in signals and systems theory and their applications in signal processing, communications, control and optimization. Topics include: Linear Vector Spaces and Metric Spaces; Hilbert Spaces: The Projection Theorem, Approximations and Orthogonal Expansions; Riemann and Lebesgue Integration and Properties; Dual Spaces and Applications to Constrained Optimization; Distribution Theory, the Schwartz Space, and the Delta Function; The Discrete Fourier Transform and the Continuous Fourier Transform; Linear Systems and their Properties; Optimization of Functionals; Applications in Signal Processing and Systems Theory.
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Introduction + Preliminary Linear Vector Spaces Normed Linear Spaces Hilbert Spaces Approximation Least Squares Estimation Dual Spaces - Linear Functionals Hahn-Banach Theorem Linear Operators and Adjoints Optimization of Functionals - Local Theory Optimization of Functionals - Global Theory Constrained Optimization Distributions and Fourier Transforms* Project Presentations ECTS - Workload Table: Activities Number Hours Workload Homework 5 10 50 Course hours 14 3 42 Project (including preparation and presentation if applicable) 1 50 50 Project Interview 1 1 1 Project Presentation 1 1 1 Preparation for the presentation 1 10 10 Total Workload: 154 Total Workload / 30: 154 / 30 5.13 ECTS Credits of the Course: 5 Type of Course: Lecture