Informations du cours

Harmonic Analysis, mathematical procedure for describing and analyzing phenomena of a periodically recurrent nature. These are the first words of the corres- ponding article in the Encyclopaedia Britannica. What does this mean? The core idea of harmonic analysis is the representation of arbitrary periodic functions as superposition of small waves. The decisive factor is here that the frequencies of the waves are integer multiples of a fundamental frequency. In music, sound waves with this kind of structure are called harmonics. Referring to music, the decomposition of a function into waves is called harmonic analysis.

Contents

The course provides an introduction into Harmonic Analysis. In particular, the following topics will be covered.

• Analysis of periodic functions via Fourier series
• Numerical methods (FFT and NFFT)
• Analysis of non-periodic functions via the Fourier transform
• Extension to generalized functions and distributions
• Fourier transform of measures