Applied & Computational Harmonic Analysis: Lecture Slides Page (Spring 2023)


  • Lecture 01: Overture / Motivations / What Is a Signal? (Monday, Apr. 3)
  • Lecture 02: Basics of Fourier Transforms (Wednesday, Apr. 5)
  • Lecture 03: Uncertainty Principles (Monday, Apr. 10)
  • Lecture 04: Discretization via Sampling (Wednesday, Apr. 12)
  • Lecture 05: Fourier Series on Intervals (Monday, Apr. 17)
  • Lecture 06: Functions of Bounded Variations; Fourier Series on Intervals II (Wednesday, Apr. 19)
  • Lecture 07: Discrete Fourier Transform (Monday, Apr. 24)
  • Lecture 08: Fast Fourier Transform (Wednesday, Apr. 26)
  • Lecture 09: From Sturm-Liouville Theory to Discrete Cosine/Sine Transforms (Monday, May 1)
  • Lecture 10: Karhunen-Loève Transform/Principal Component Analysis (Wednesday, May 3)
  • Lecture 11: Time-Frequency Analysis and Synthesis; Windowed (or Short-Time) Fourier Transform (Monday, May 8)
  • Lecture 12: Introductory Frame Theory; The Balian-Low Theorem (Wednesday, May 10)
  • Lecture 13: Continuous Wavelet Transforms (Monday, May 15)
  • Lecture 14: Continuous Wavelet Transforms II and the supplementary slides on Analytic Signal (Wednesday, May 17)
  • Lecture 15: Discrete Wavelet Transforms; Multiresolution Approximation; Scaling Functions (Monday, May 22)
  • Lecture 16: Conjugate Mirror Filters; Mother Wavelets; Orthonormal Wavelet Basis (Wednesday, May 24)
  • Lecture 17: Vanishing Moments; Support Size; Regularity; and Daubechies's Compactly Supported Wavelets (Wednesday, May 31)
  • Lecture 18: Fast Wavelet Transforms; Various Extensions (Monday, Jun. 5)
  • Lecture 19: A Library of Orthonormal Bases and Adapted Signal Analysis (Wednesday, Jun. 7)
  • Supplementary Lecture: Multiscale Basis Dictionaries on Graphs and Networks

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