The discrete wavelet transform (DWT) is usually carried out by filterbank iteration; however for a fixed number of zero moments this does not yield a discrete-time basis that is optimal with respect to time localization. This paper discusses the implementation and properties of an orthogonal DWT with two zero moments and with improved time localization. The basis is not based on interbank iteration; instead different filters are used for each scale. For coarse scales the support of the discrete-time basis functions approaches two thirds that of the corresponding functions obtained by interbank iteration. This basis which is a special case of a class of bases described by Alpert retains the octave-band characteristic and is piecewise linear (but discontinuous). Closed-form expressions for the filters are given an efficient implementation of the transform is described and improvement in a denoising example is shown. This basis being piecewise linear is reminiscent of the slant transform to which it is compared.
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering