The slantlet transform-a discrete wavelet transform of approximation order 2 with improved time-localization

Research output: Contribution to journalArticlepeer-review

Abstract

The discrete wavelet transform is usually carried out by filter bank iteration; however, for a fixed approximation order, this does not yield a discrete-time basis that is optimal with respect to time-localization. This paper describes new orthogonal discrete wavelet transform with approximation order two and improved time-localization. It is not based on filter bank iteration; instead, new 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 filter bank iteration. The new basis retains the octave-band characteristic and leads cleanly to a DWT for finite-length signals. Closed-form expressions for the filters are given, an efficient implementation of the transform is described, and improvement in a denoising example is shown. The basis, being piecewise linear, is reminiscent of the slant transform with which it is compared.

Original languageEnglish (US)
Number of pages1
JournalIEEE Transactions on Signal Processing
Volume46
Issue number6
StatePublished - 1998

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'The slantlet transform-a discrete wavelet transform of approximation order 2 with improved time-localization'. Together they form a unique fingerprint.

Cite this