• A bio-geometric model for sound reconstruction
  • Rand ASSWAD
  • Acknowledgements
  • 1 Introduction
    • 1.1 Laboratory and supervision
    • 1.2 Internship mission
  • 2 Image reconstruction model
    • 2.1 Neoro-geometric model of V1
    • 2.2 Wilson-Cowan model in V1
  • 3 Sound reconstruction model
    • 3.1 From V1 to A1
    • 3.2 Sound reconstruction pipeline
    • 3.3 Time-Frequency representation
      • 3.3.1 The Short-Time Fourier Transform
      • 3.3.2 Time and frequency shifts operators
      • 3.3.3 Discrete STFT
      • 3.3.4 STFT windowing
      • 3.3.5 Uncertainty principle and resolution issues
      • 3.3.6 Inverse Short-Time Fourier Transform
      • 3.3.7 Griffin-Lim Algorithm
    • 3.4 The lift to the augmented space
      • 3.4.1 The sound chirpiness
      • 3.4.2 Single time-varying frequency
      • 3.4.3 Control system
      • 3.4.4 Lift to the contact space
      • 3.4.5 Lift implementation
    • 3.5 Cortical activations in A1
  • 4 Implementation
    • 4.1 The WCA1.jl library
      • 4.1.1 The STFT module
      • 4.1.2 Optimizing the lift module
    • 4.2 Results
  • 5 Conclusion
    • 5.1 Reviewing the model
      • 5.1.1 Model analysis
      • 5.1.2 Wavelet transform
      • 5.1.3 The lift operator
      • 5.1.4 The group representation
      • 5.1.5 The WCA1.jl package
      • 5.1.6 A sparse lift implementation
    • 5.2 Acquired knowledge
    • 5.3 My future project
  • Appendix
  • A Short-Time Fourier Transform
    • A.1 Parseval’s formula
    • A.2 Inverse Short-Time Fourier Transform
  • B Uncertainty principle
  • C Heisenberg group
    • C.1 Heisenberg group action on the contact space
    • C.2 Introducing the chirpiness to the Heisenberg group
  • References
  • PDF book
  • HTML standalone version
  • Presentation slides
  • Github repository
  • Download source code

A bio-inspired geometric model for sound reconstruction

A bio-inspired geometric model for sound reconstruction

Master’s Thesis

Rand ASSWAD

04/01/2021 - 30/06/2021