The orthonormal basis generated by a wavelet of L(R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L(R) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized...

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

We analyze the time-frequency concentration of the Gabor orthonormal basis G(f, 1, 1) constructed by Høholdt, Jensen, and Justesen. We prove that their window function f has near optimal time and frequency localization with respect to a non-symmetric version of the Balian-Low Theorem. In particular, we show that if (p, q) = (3/2, 3), then R |t| |f(t)|dt < ∞ and R |γ| | b f(γ)|dγ < ∞, for 0 < ≤ ...

We analyze the time-frequency concentration of the Gabor orthonormal basis G(f,1,1) constructed by Høholdt, Jensen, and Justesen. We prove that their window function f has near optimal time and frequency localization with respect to a non-symmetric version of the Balian-Low Theorem. In particular, we show that if (p, q) = (3/2,3), then R |t||f(t)|dt < ∞, and R |γ|| b f(γ)|dγ < ∞, for 0 < ǫ ≤ 3/...

In this paper, we study the properties of the transform which approximates a signal at a given resolution. We show that the difference of a signal at different resolutions can be extracted by decomposing the signal on a wavelet orthonormal basis. In wavelet orthonormal basis is a family of functions, which is built by dilating and translating a unique function. The development of orthonormal wa...

Any non-complete orthonormal system in a Hilbert space can be transformed into basis by small perturbations.

We present a direct proof of a known result that the Hardy operator Hf(x) = 1 x R x 0 f(t) dt in the space L = L2(0,∞) can be written as H = I − U , where U is a shift operator (Uen = en+1, n ∈ Z) for some orthonormal basis {en}. The basis {en} is constructed by using classical Laguerre polynomials. We also explain connections with the Euler differential equation of the first order y′− 1 x y = ...

The hidden subgroup problem (HSP) provides a unified framework to study problems of grouptheoretical nature in quantum computing such as order finding and the discrete logarithm problem. While it is known that Fourier sampling provides an efficient solution in the abelian case, not much is known for general non-abelian groups. Recently, some authors raised the question as to whether post-proces...

In this paper, model sets for continuous{time linear time invariant systems that are spanned by xed pole orthonormal bases are investigated. These bases gen-eralise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H p ((); 1 p < 1 and the right half plane algebra A(() provided that a mild condition on the choice of basis p...