Time-Frequency Analysis
Gabor frames, short-time Fourier transforms, and modulation spaces.
Time-Frequency Analysis. Gabor frames, short-time Fourier transforms, and modulation spaces.
Foundations and canonical references
The standard treatments of time-frequency analysis approach the subject from complementary angles. Grochenig, Foundations of Time-Frequency Analysis (2001) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Boggiatto, Time-Frequency Analysis (2008) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for time-frequency analysis include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2001Foundations of Time-Frequency Analysisgrochenig-2001
- textbook · supporting · 2008Time-Frequency Analysisboggiatto-2008
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