Search results for "ignal processing"
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Sing and Measure: Sound as Voice as Quanta
2022
The universal concept of a “music of the spheres” traverses the history of philosophy, science and art, from Pythagoras to Kepler and beyond. In modern times, a sphere in three dimensions—the Bloch sphere—is used to illustrate the state of a qubit, the basic unit of quantum information. On the same spherical surface, the fundamental components of voice production can be located, so that any utterance can be seen as the evolution of a unit two-dimensional vector having complex coefficients. Indeed, any sound can be analyzed and decomposed into overlapping sinusoidal components, broadband noises, and impulsive transients, which in turn can be associated to fundamental means of vocal sound pro…
Relationship between volume and energy of vector fields
2001
Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields
Deformation Quantization in White Noise Analysis
2007
We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.