Multi-Resolution Analysis and Wavelets
Lecture 1
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Time-Frequency 1: This lecture provides an introduction to time-frequency analysis and the Gabor transform, or short-time Fourier transform.
Lecture 2
Time-Frequency 2: This lecture introduces wavelet transforms and their mathematical properties. Further, a formal architecture for a multi-resolution analysis is given in the second part of the lecture.
Lecture 3
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Time-Frequency 3: This lecture implements a basic Gabor transform and shows how to construct a spectrogram.
KEY REFERENCES
J. N. Kutz, NOTES — CHAPTER 13 (Kutz, Data-Driven Modeling & Scientific Computation, Oxford 2013)
S. Mallat, A Wavelet Tour of Signal Processing — The Sparse Way (Academic Press, 3rd Edition, 2009)