TimeFrequencyWaveforms Documentation

Author: Christopher J. Moore

A fast, JAX-based Python package to take the wavelet transforms of harmonic-based GW waveform model.

Two types of transform are possible: one that transforms from the time-domain (TD) to the time-frequency domain (TFD), i.e. the TD \(\rightarrow\) TFD transform; and another that transforms from the frequency-domain (FD) to the time-frequency domain (TFD); i.e. the FD \(\rightarrow\) TFD transform. Currenlty, only the TD \(\rightarrow\) TFD transform is implemented.

The project lives on GitHub.

Mathematical Background:

• Mathematical Background
  • Introduction
  • WDM Wavelets
  • Fast Wavelet Transform (TD \(\rightarrow\) TFD)
  • Fast Wavelet Transform (FD \(\rightarrow\) TFD)
  • References
  • Appendices
  • Appendix A: Derivation of Time-Shift Properties
  • Appendix B: Derivation of Freq-Shift Properties

Package Contents:

• TimeFrequencyWaveforms.code.utils module
  • Xn()
  • cnm()
  • snm()
  • chatnm()
  • shatnm()
  • row_roll()
• TimeFrequencyWaveforms.code.TD_to_TFD_transform module
  • Transformer
    • Transformer.__init__()
    • Transformer.make_grids()
    • Transformer.make_interpolators()
    • Transformer.coeffs()
    • Transformer.cnm_snm()
    • Transformer.transform()
• TimeFrequencyWaveforms
  • TimeFrequencyWaveforms package
    • Subpackages
      • TimeFrequencyWaveforms.code package
        • Submodules
          • TimeFrequencyWaveforms.code.TD_to_TFD_transform module
            • Transformer
          • TimeFrequencyWaveforms.code.utils module
            • Xn()
            • cnm()
            • snm()
            • chatnm()
            • shatnm()
            • row_roll()
• Example Notebooks
  • Getting Started
  • EMRI Example with FEW

Code Repository:

• GitHub