This course is a prerequisite for Computer Graphics and Image Processing, Artificial Intelligence I, Artificial Intelligence II (Part II), Computer Vision (Part II), Information Theory and Coding (Part II), Quantum Computing (Part II), Digital Signal Processing (Part II).
Aims
The aims of this course are to review some key concepts and operations
defined in continuous mathematics involving real and complex-valued
functions. Focus is on the use and implementation of these notions as
encountered in computer science.
Lectures
Review of analysis.
Limits, continuity and differentiability. Power series
and transcendental functions. Taylor series. Complex
variables.
Fourier series.
Introduction. General properties. Uses and
applications.
Basis functions and decompositions.
Expansions and basis functions. Orthogonality, inner
products and completeness. Useful expansion bases for
functions.
Representation of signals.
Fourier transforms and their inverses: introduction
and general properties. Uses and applications. Brief
introduction to wavelet analysis and its comparison
with Fourier analysis.
Objectives
At the end of the course students should
understand how functions can be
represented in terms of their projections onto basis
functions
be fluent in the use and properties of
complex variables and power series
grasp key properties and uses of Fourier
analysis, transforms, and wavelets
Reference books
* Oppenheim, A.V. & Willsky, A.S. (1997). Signals
and systems. Prentice-Hall.
Pinkus, A. & Zafrany, S. (1997). Fourier series and integral
transforms. Cambridge University Press.
Stephenson, G. (1973). Mathematical methods for science
students. Addison Wesley Longman.
