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