Wavelets- A Mathematical Microscope

Explore the powerful world of wavelet transform in this comprehensive 34-minute video. Delve into the revolutionary method that uncovers hidden structures in signals, applicable across various fields from hydrodynamics to neuroscience. Learn how to build a wavelet toolkit step-by-step, starting with an introduction to time and frequency domains, Fourier Transform, and its limitations. Discover the concept of wavelets as localized functions, their mathematical requirements, and the Real Morlet wavelet. Gain insights into wavelet transform overview, mother wavelet modifications, and computing local similarity. Understand complex topics such as function dot products, convolution, and complex numbers. Visualize wavelet analysis through scalograms and grasp the concept of uncertainty with Heisenberg boxes. Conclude with a recap of this invaluable signal processing tool, presented by computational neuroscience student and researcher Artem Kirsanov from Moscow State University.

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