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This introductory course explains how wavelet transforms decompose signals across time and frequency to reveal structure hidden by noise. It develops the method through Fourier-transform limitations, localized Morlet wavelets, convolution, scalograms, and Heisenberg boxes.
Syllabus
Introduction
Time and frequency domains
Fourier Transform
Limitations of Fourier
Wavelets - localized functions
Mathematical requirements for wavelets
Real Morlet wavelet
Wavelet transform overview
Mother wavelet modifications
Computing local similarity
Dot product of functions?
Convolution
Complex numbers
Wavelet scalogram
Uncertainty & Heisenberg boxes
Recap and conclusion
Taught by
Artem Kirsanov