Discrete wavelet transform

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Discrete wavelet transform: main concepts

1 Main concepts

The haar system as an example of dwt

A hierarchy of detail in the haar system

Haar approximation at the kth coarseness level

The scaling equation

The wavelet scaling equation

Conditions on h[n] and g[n]

Values of g[n] and h[n] For the haar system

Wavelets: a countable orthonormal basis for the space of square-integrable

Filterbanks interpretation of the discrete wavelet transform

Initialization of the wavelet transform

Regularity conditions, compact support, and daubechies' wavelets

Computing the scaling function: the cascade algorithm

Finite-length sequences and the dwt matrix

Dwt implementation using ffts

Dwt applications - choice of phi(t)

Dwt application - de-noising

Source: OpenStax, Digital signal processing (ohio state ee700). OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10144/1.8

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