Lecture Notes (Signals and Systems)

 Bahman Gharesifard Fall 2013

The main reference for this course is the book (A Mathematical Introduction to Signals and Systems, by Andrew D. Lewis). Lecture notes are provided here, mainly to guide you through the book. A major part of the materials presented in these notes are the expanded versions of the slides previously used to teach this course by Andrew. Of course, at times, we might trade precision for intuition (bad practice), but hopefully this note helps answering the question: which parts of these two volumes do I need to know about? As you will realize, our journey through this book is in not chronological; we rather adapt an efficient path which would allow us to grab enough structures from different chapters in order to be able to study signals (and systems). Please visit Outlines to know more about this course.

Lecture Notes:

 Lecture 1 (What are signals?) Lecture 2 (Signals in time domain?) Lecture 3 (Algebraic structure of signals) Lecture 4 (Infinite dimensional vector spaces) Lecture 5 (Normed vector spaces I) Lecture 6 (Normed vector spaces II) Lecture 7 (Banach spaces) Lecture 8 (Completion of normed vector spaces I) Lecture 9 (Completion of normed vector spaces II) Lecture 10 (Topology of normed vector spaces) Lecture 11 (Hilbert Spaces) Lecture 12 (Continuous-time signal spacesI) Lecture 13 (Continuous-time signal spacesII) Lecture 14 (Continuous-time signal spacesIII) Lecture 15 (Continuous-time signal spacesIV) Lecture 16 (The Riemann integral) Lecture 17 (The Lebesgue measure) Lecture 18 (Borel sets) Lecture 19 (The Lebesgue integral) Lecture 20 (Summary of discrete and continuous-time signal spaces) Lecture 21 (Introduction to Fourier transforms I) Lecture 22 (Introduction to Fourier transforms II) Lecture 23 (Properties of CDFT) Lecture 24 (Inversion of CDFT) Lecture 25 (Pointwise convergence of CDFT I) Lecture 26 (Pointwise convergence of CDFT II) Lecture 27 (Uniform convergence of CDFT) Lecture 28 (The continuous-continuous Fourier transform) Lecture 29 (Properties of CCFT) Lecture 30 (Properties of CCFT II) Lecture 31 (The discrete-continuous Fourier transform) Lecture 32 (The discrete-continuous Fourier transform II) Lecture 33 (The discrete-discrete Fourier transform)

For questions, contact me with bahman at mast.queensu.ca or with 613-533-2441 (I prefer emails)