It will start with the history (shortly) of Fourier Analysis, including names like Fejer, and end up with Gabor and TF-analysis hidden in JPEG, MP3 etc.., cf. the Jarnick Lecture in Oct. 2017 in Prague! hgfei

OFFICIAL ABSTRACT:
Although each of us is using modern technology (mobile phones, digital radio, television, digital cameras
and so on) regularly in our daily life few people are aware of the fact how much this technology
is based on important mathematical ideas going back to the theory of J. B. Fourier, first proposed in
1822 in a paper describing the solution of the heat equation. The classical theory of Fourier series
was focussing very much on questions around the pointwise convergence of Fourier series, with
important Hungarian contributions (starting with L. Fejer). The last century saw the development of
the theory of Fourier transforms (of a continuous variable) and based on it the concept of Abstract
Harmonic Analysis. For real world applications, however, we think that methods from time-frequency
analysis (TFA) also very relevant. The central object is the STFT (Short-Time Fourier Transform),
which describes the development of the local frequency spectrum over time. We will demonstrate in
which sense this modern theory allows to discuss problems of current interest (e.g. questions arising
in mobile communication or musicology) and how in the last 40 years a very active field of research
close to those applications has emerged.
Dr