Publication

Nonseparable 2-dimensional and 3-dimensional wavelets

Martin Vetterli
1995
Journal Articles

Abstract

We present two- and three-dimensional nonseparable wavelets. They are obtained from discrete-time bases by iterating filter banks. We consider three sampling lattices: quincunx, separable by two in two dimension, and FCO. The design methods are based either on cascade structures or on the McClellan transformation in the quincunx case. We give a few design exemples. In particular, the first example of an orthogonal 2-D wavelets basis with symetries is constructed.

Official source

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Martin Vetterli
1995
Journal Articles

Abstract

Official source

Related concepts (15)

Discrete wavelet transform

In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.

Filter bank

In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal.

Related publications (1)

Nonseparable 2-dimensional and 3-dimensional wavelets

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