Language Centre (UCL)
Coding and
transformations
UCL Mathematics Program for EFREI students
Instructor:
Dr. A.V. Salsac (a.salsac@ucl.ac.uk)
Lectures: 2 hours a week for
8 weeks
(for each group)
Attendance: mandatory
(attendance list sent to EFREI)
Evaluation: Quizzes
throughout the term and one final exam
Syllabus
Chapter 1: Introduction
Fourier series (periodic functions)
Chapter 2: Fourier Transforms
Fourier transforms
Definition and
properties
Convolution
Common Fourier transforms (Dirac delta
functions, Dirac combs, sinusoidal functions (sine, cosine), periodic
functions, window functions)
Power and energy
spectrum,
Introduction to
Fast Fourier Transform (FFT) algorithm
Discrete Fourier Transforms (FT(DFT) to
2D FT) and to 1D or 2D discrete cosine transforms
Chapter 3: Application to Signal Sampling
Sampling, decimation and
interpolation
The
Nyquist-Shannon-Kotelnikov sampling theorem
Filtering and
down-sampling of temporal (spatial) samples
Interpolation