Dealing with data in a well-adapted representation space is a key for understanding, modifying or compressing observed signals. In nonstationary situations where spectral features are considered as varying over time, combining the—usual but mutually exclusive—time and frequency variables offers such a natural framework which formalizes the intuitive idea of a musical score. Sounds are transformed this way as readable images in a joint time-frequency plane and, conversely, time-frequency patterns can be turned into audible waveforms. As it is the rule in signal processing, with the Fourier analysis as the most prominent example in a stationary setting, the ‘art of time-frequency analysis’ is to design and use meaningful, well-defined and efficient tools which lie at the intersection of physics, applied mathematics and computer science, even when stationarity does not hold anymore. In this lecture, basics of classical time-frequency analyses will be briefly recalled, and recent advances related respectively to varying frequencies, localized oscillations and possibly non-harmonic modes will be discussed more specifically, as three ways of going beyond the classical Fourier analysis whose publication is just celebrating this year its 200th anniversary.
Patrick Flandrin received the engineer degree from ICPI Lyon, France, in 1978, and the Doct.-Ing. and Docteur d’État degrees from INP Grenoble, France, in 1982 and 1987, respectively. He joined CNRS in 1982, where he is currently Research Director. Since 1991, he has been with the Signals, Systems and Physics Group, within the Physics Department at ENS de Lyon, France. He has been President of GRETSI, the French Association for Signal and Image Processing, from 2009 to 2019. His research interests include mainly nonstationary signal processing (with emphasis on time-frequency and time-scale methods), scaling stochastic processes and complex systems. He authored two monographs in those areas, the most recent one being Explorations in Time-Frequency Analysis (Cambridge University Press, 2018). Dr. Flandrin was awarded the Philip Morris Scientific Prize in Mathematics (1991), the SPIE Wavelet Pioneer Award (2001), the Prix Michel Monpetit from the French Academy of Sciences (2001), the Silver Medal from CNRS (2010), and the Technical Achievement Award from the IEEE Signal Processing Society (2017). Past Distinguished Lecturer of the IEEE Signal Processing Society (2010-2011), he is a Fellow of the IEEE (2002) and of EURASIP (2009). Elected member of the French Academy of Sciences in 2010, he is currently its President for the period 2021-2022.