Author_Institution :
Electr. Eng., Polytech. Univ., Brooklyn, NY, USA
Abstract :
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 filterbank 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 filterbank iteration. This basis, which is a special case of a class of bases described by Alpert (1992, 1993), 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
Keywords :
channel bank filters; discrete wavelet transforms; filtering theory; noise; signal representation; signal resolution; closed-form expressions; coarse scales; data smoothing; denoising; discrete wavelet transform; discrete-time basis functions; filterbank iteration; multiresolution decomposition; octave-band characteristic; orthogonal DWT; piecewise linear basis; signal representation; slant transform; slantlet transform; time localization; zero moments; Bandwidth; Closed-form solution; Discrete transforms; Discrete wavelet transforms; Filter bank; Noise reduction; Piecewise linear techniques; Signal design; Smoothing methods; Wavelet transforms;
