wavelets.md

Background

• The term 'wavelet' refers to a brief, wave-like oscillation of amplitude ($y$) against time ($x$).
  • The amplitude begins at $0$, pulses away one or more times, and returns to end at $0$.
• There are many 'families' of wavelets (broadly on the specific number and shape of the constituent pulses).
• There are also many use cases, including for our purposes of data compression.

Task

• Type: Exploration
• Task: Explore the 'pywavelets' wavelet library using either or both of
  • the Wavelet browser
  • a local copy of the library (import pywavelets, note, renamed from pwyt)
• Bonus:
  • Implement (re-create) one or more wavelets from scratch.
  • Demonstrate the properties of a given wavelet (e.g., integral sum to 0).

Also on this repository

This exercise is exploratory. Optionally, you can also demonstrate the two properties above.

For other, related exercises, click below for:

• the mathematics of the Haar wavelets
• some aspects of the application of Wavelets to JPEG-2000