Unified construction of fractional generalized orthogonal bases

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Synthesis of fractional Laguerre basis for system approximation

Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to quickly capture the aperiodic multimode behavior with a limited number of terms. Hence, fractional orthogonal bases are expected to better approximate fractional models with fewer parameters. Intuit...

New construction of mutually unbiased bases in square dimensions

We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k, s)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bound...

Construction of fractional spline wavelet bases

We extend Schoenberg's B-splines to all fractional degrees α > − 2 . These splines are constructed using linear combinations of the integer shifts of the power functions x+ α (one-sided) or x * α (symmetric); in each case, they are αHölder continuous for α > 0. They satisfy most of the properties of the traditional B-splines; in particular, the Riesz basis condition and the two-scale relation, ...

Orthogonal quincunx wavelets with fractional orders

We present a new family of 2D orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order α, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of L2(R) for any α > 0. The wavelets are fractional in the sense that the app...