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Ternary wavelets and their applications to signal compression

100%

Mustafa G., Chen F., Huang Z.

International Journal of Applied Mathematics and Computer Science

2004

tom 14

nr 2

233-240

We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even ternary' wavelets. Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than four-point wavelets. These ternary wavelets are locally supported, symmetric and stable. The analysis and synthesis algorithms have linear time complexity.

A necessary and sufficient condition for the existence of a father wavelet

100%

Gripenberg G.

Studia Mathematica

1995

tom 114

nr 3

207-226

It is proved that if ${2^{-m/2} ψ(2^{-m} • - k)}_{m,k ∈ ℤ}$ is an orthonormal basis in $L^2(ℝ;ℂ)$, then the mother wavelet ψ is obtained from a multiresolution generated by a father wavelet if and only if $∑_{p=1}^{∞| ∑_{k ∈ ℤ} |ψ̂(2^{p}(• + k))|^2 > 0$ a.e.

Wavelet bases in $L^{p}(ℝ)$

88%

Gripenberg G.

Studia Mathematica

1993

tom 106

nr 2

175-187

It is shown that an orthonormal wavelet basis for $L^2(ℝ)$ associated with a multiresolution is an unconditional basis for $L^p(ℝ)$, 1 < p < ∞, provided the father wavelet is bounded and decays sufficiently rapidly at infinity.

Ograniczanie wyników

2 Studia Mathematica

1 International Journal of Applied Mathematics and Computer Science

2 Gripenberg G.

1 Chen F.

1 Huang Z.

1 Mustafa G.

1 2004

1 1995

1 1993

Wyniki wyszukiwania

Ternary wavelets and their applications to signal compression

A necessary and sufficient condition for the existence of a father wavelet

Wavelet bases in $L^{p}(ℝ)$