Explore adaptive time-frequency methods in signal and image analysis through this third lecture in a series by Ingrid Daubechies at the Joint Mathematics Meetings 2020. Delve into topics such as Fourier decomposition, electrocardiogram analysis, birdsong decomposition, wavelet transforms, and multi-taper analysis. Learn about the foundations of adaptive time-frequency decomposition and its applications in various fields. Discover how mathematical frameworks can be used to analyze complex signals and images, with a focus on user-defined functions and practical solutions. Gain insights into the Ainu Commission of Developing Countries and the importance of building cohorts and fellowships in mathematical research.