This paper presents a novel two-dimensional split-vector-radix fast-Fourier-transform (2D svr-FFT) algorithm. The modularizing feature of the 2D svr-FFT structure enables us to explore its characteristics by identifying the local structural property. Each local module is designated as a DFT (non-DFT) block if its output corresponds to DFT (non-DFT) values. The block attribute (DFT or non-DFT) d...

We construct Dirac operators and spectral triples for certain, not necessarily selfsimilar, fractal sets built on curves. Connes’ distance formula of noncommutative geometry provides a natural metric on the fractal. To motivate the construction, we address Kigami’s measurable Riemannian geometry, which is a metric realization of the Sierpinski gasket as a self-affine space with continuously dif...

We study the convergence of resistance metrics and forms on a converging sequence spaces. As an application, we existence uniqueness self-similar Dirichlet Sierpinski gaskets with added rotated triangle. The fractals depend parameter in continuous way. When is irrational, fractal not post critically finite (p.c.f.), there are infinitely many ways that two cells intersect. In this case, define f...

Fractals contain an infinite number of scaled copies of a starting geometry. Due to this fundamental property, they offer multiband characteristics and can be used for miniaturization of antenna structures. In this paper, electromagnetic transmission through fractal shaped apertures in an infinite conducting screen has been investigated for a number of fractal geometries like Sierpinski gasket,...

We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral...

We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine mappings. We build a duality for such systems by scaling in two directions: fractals in the small by contractive iterations, and fractals in the large by recu...