7.00.02 - Background - Aster Analytics

Teradata Aster® Analytics Foundation User GuideUpdate 2

Product
Aster Analytics
Release Number
7.00.02
Published
September 2017
Content Type
Programming Reference
User Guide
Publication ID
B700-1022-700K
Language
English (United States)
Last Update
2018-04-17

DWT is a time-frequency analysis tool for which the wavelets are discretely sampled. DWT is different from the Fourier transform, which provides frequency information on the whole time domain. A key advantage of DWT is that it provides frequency information at different time points.

Mallat's algorithm can be described as a series of iterative steps. For example, for a 3-level wavelet transform:

  1. Use S(n) as the original time domain sequence as the input of level 1.
  2. Convolve the input sequence with high-pass filter h(n) and low-pass filter g(n).

    The two generated sequences are the detail coefficients D k and the approximation coefficients A k in level k.

  3. If current level k is the maximum transform level n, stop; otherwise, use A k as the input sequence for the next level (that is, increment k by 1 and go to step 2.)