Music scholars have been intensively studying tonal harmony for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of Western tonal harmony, which builds on well-known theories of tonal harmony. In contrast to many o...

This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so called Siegel-Jacobi space that is important arithmetically and geometrically. We present some new results on the Siegel-Jacobi space.

one of the important factors influencing outdoor insulators performance is pollution phenomenon. the pollution, especially during humidity condition, reduces superficial resistance of insulator and lead to a flow of leakage currents (lc) on the insulator surface, which may result in total flashover. the lc characteristics are affected by parameters such as nature and severity of pollution. loca...

This paper describes a multi-pitch analysis method using specmurt analysis with iterative estimation of the quasioptimal common harmonic structure function. Specmurt analysis (Sagayama et al., 2004) is based upon the idea that superimposed harmonic structure pattern can be expressed as a convolution of two components, a fundamental frequency distribution and a ‘common harmonic structure’ functi...

In [4], D. Osipov and A. Parshin developed an approach to harmonic analysis on higher dimensional local fields through categories of filtered vector spaces as in [3]. In the present paper we give a variant of this approach that behaves nicely for inductive arguments. We establish Pontryagin duality, the Fourier inversion formula, and a Plancherel formula for all dimensions. ∗This paper was writ...

This paper studies the Laplacian operator on a metrized graph, and its spectral theory.

In the present survey we discuss various applications of methods and ideas of harmonic analysis in problems of geometric discrepancy theory and irregularities of distribution. A great number of analytic tools (exponential sums, Fourier series, Fourier transform, orthogonal expansions and wavelets, Riesz products, Littlewood–Paley theory, Carleson’s theorem) have found applications in this area....

There are a large number of frequency-domain analysis methods that are in widespread use. The most popular of these are frequency scans, harmonic penetration, and harmonic power flow. Each of these techniques can be employed on a “per-phase” (positive or zero sequence) or “multi-phase” basis and each technique utilizes an admittance matrix system model developed from individual component-level ...

Prior to installation of a large harmonic load it is necessary to conduct a harmonic analysis using computer simulation in order to pr"iirt possible negative effects of harmonics' The 'problem is that many parameters are unknown and need to be assumed. One of these are existing or background harmonic levels. Tthe paper describes the resubs of harmonic measurements as Qn inclication of existing ...