Credits: 9

Type: advanced and professional

Objectives:

Basic principles of harmonic analysis and applications in different fields of science and technical science, combining mathematical rigour with the practical uses of Fourier analysis.

Knowledge:

• Historical background.
• Discrete Fourier transform, Fourier series and transform of the continuous time signal and distributions. FFT.
• The uncertainty principle.
• Time-limited and band-limited signals, sampling and filters.
• The Paley-Wiener theorem, Hardy functions.
• Applications to sound and image treatment, Fourier optics and computed tomography (TAC).
• Multiresolution analysis to localise signals in time and with frequency.

Subject-specific competences:

To show a thorough and practical understanding of modern techniques of harmonic analysis as applied in different fields, such as in the application to wavelets and in current methods of image diagnosis for medical purposes, with the use of computer tools to perform effective numerical operations with signals.