Browsing by Keywords "Phase space methods"
Now showing items 113 of 13

Canonicalcovariant Wigner function in polar form
(OSA  The Optical Society, 2000)The twodimensional Wigner function was investigated in polar canonical coordinates. The covariance properties under the action of affine canonical transformations were derived. The polar canonical phasespace representations ... 
Degrees of freedom of optical systems and signals with applications to sampling and system simulation
(Optical Society of America, 2013)We study the degrees of freedom of optical systems and signals based on spacefrequency (phase space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the spacefrequency ... 
Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the spacebandwidth product
(Optical Society of America, 20100730)Linear canonical transforms (LCTs) form a threeparameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique ... 
The fractional fourier transform
(IEEE, 2001)A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phasespace representations (time or spacefrequency representations) and the concept of fractional Fourier domains are ... 
The Fractional Fourier transform and harmonic oscillation
(Springer, 2002)The athorder fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zerothorder fractional Fourier transform operation is equal to the identity operation and the firstorder ... 
Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems
(IEEE, 2014)We study the degrees of freedom of optical systems and signals based on spacefrequency (phasespace) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the spacefrequency ... 
Nonlocal, noncommutative picture in quantum mechanics and distinguished continuous canonical maps
(IOP Science, 2002)It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate hindependent quantum nonlinear canonical ... 
Nonorthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms
(Elsevier BV * NorthHolland, 19951015)It is customary to define a phase space such that position and momentum are mutually orthogonal coordinates. Associated with these coordinates, or domains, are the position and momentum operators. Representations of the ... 
Phasespace window and degrees of freedom of optical systems with multiple apertures
(Optical Society of America., 2013)We show how to explicitly determine the spacefrequency window (phasespace window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the ... 
Quantum canonical transformations in starproduct formalism
(IOP, 2013)We study construction of the starproduct version of three basic quantum canonical transformations which are known as the generators of the full canonical algebra. By considering the fact that starproduct of cnumber ... 
Quantum Dynamics of LongRange Interacting Systems Using the PositiveP and GaugeP Representations
(American Physical Society, 2017)We provide the necessary framework for carrying out stochastic positiveP and gaugeP simulations of bosonic systems with longrange interactions. In these approaches, the quantum evolution is sampled by trajectories in ... 
Stridetostride energy regulation for robust selfstability of a torqueactuated dissipative springmass hopper
(A I P Publishing LLC, 2010)In this paper, we analyze the selfstability properties of planar running with a dissipative springmass model driven by torque actuation at the hip. We first show that a twodimensional, approximate analytic return map ... 
Wignerrelated phase spaces for signal processing and their optical implementation
(Optical Society of America, 2000)Phase spaces are different ways to represent signals. Owing to their properties, they are often used for signal compression and recognition with high discrimination abilities. We present several recently introduced ...