Arbitrary Quantization Research Articles

Quantization of FIR filters under a total integer cost constraint

In this paper, we present computationally efficient algorithms for obtaining a particular class of optimal quantized representations of finite-impulse response (FIR) filters. We consider a scenario where each quantization level is associated with a certain integer cost and, given an FIR filter with real coefficients, our goal is to find the quantized representation that minimizes a certain error criterion under a constraint on the total cost of all quantization levels used to represent the filter coefficients. We first formulate the problem as a constrained shortest path problem and discuss how an efficient dynamic programming algorithm can be used to obtain the optimal quantized representation for arbitrary quantization sets. We then develop a greedy algorithm which has even lower computational complexity and is shown to be optimal when the quantization levels and their associated costs satisfy a certain, easily checkable criterion. For the special case of the quantization set that involves levels that are sums of signed powers-of-two and whose cost is captured by the number of powers of two used in their representation, the total integer cost relates to the cost of the very large-scale integration implementation of the given FIR filter and our analysis clarifies the optimality of previously proposed algorithms in this setting.

Arbitrary trajectory quantization method.

The arbitrary trajectory quantization method (ATQM) is a time dependent approach to quasiclassical quantization based on the approximate dual relationship that exists between the quantum energy spectra and classical periodic orbits. It has recently been shown however, that, for polygonal billiards, the periodicity criterion must be relaxed to include closed almost-periodic (CAP) orbit families in this relationship. In light of this result, we reinvestigate the ATQM and show that at finite energies, a smoothened quasiclassical kernel corresponds to the modified formula that includes CAP families while the delta function kernel corresponding to the periodic orbit formula is recovered as E-->infinity. Several clarifications are also provided.

On the Canonical Normalization of a Trace Density of Deformation Quantization

We describe a procedure of the canonical normalization of a formal trace density of an arbitrary deformation quantization on a symplectic manifold. We apply this procedure to give an explicit expression of the canonical formal trace density of deformation quantization with separation of variables on a pseudo-Kaahler manifold.

Nucleon structure in a relativistic quark model.

We study nucleon structure in the relativistic quark model based on the Bakamjian-Thomas construction of the Poincare generators for an arbitrary quantization surface. The one body, single particle approximation to the current operators is used to calculate electromagnetic matrix elements. The Lorentz symmetry breaking resulting from such an approximation is fully investigated. The results for the light front and instant quantization limits are detailed. A suggestion for the resolution of the quark model inability to simultaneously describe the positive neutron electric form factor, {ital G}{sup {ital n}}{sub {ital E}}({ital Q}{sup 2}) at small {ital Q}{sup 2} and the negative slope of the neutron to proton structure function ratio at large {ital x} is presented.

Algebraic index theorem

We prove the Atiyah-Singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold.

Classical resonances and an arbitrary trajectory quantization scheme for a chaotic system

The exponential decay of correlations in chaotic systems is often modulated and shows up as broad peaks in the power spectrum. For a particle sliding freely on a compact surface of constant negative curvature, we show that these classical resonances are directly related to the quantal eigenenergies of the system. We use this as the basis for proposing a quantization scheme which requires the knowledge of a single arbitrary ergodic classical trajectory. Our results are substantiated numerically.

Design methodology of decimation filters for oversampled ADC based on quadratic programming

A design methodology for oversampled analog-to-digital converter decimation filters is presented. The methodology tackles the finite-impulse-response (FIR) filter design problem by formulating a quadratic programming problem that minimizes the integral of the aliased noise subject to the passband and stopband constraints. The approach offers a design whose response is optimized to meet arbitrary quantization noise power spectral density and anti-alias requirements. Because the projected Hessian matrix of the objective function is positive definite, the quadratic function has a unique minimum. The methodology is applied to design filters for different requirements and the performance is compared to conventional approaches.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Influence of an arbitrarily oriented quantizing magnetic field on the field emission from A II3B V2 compounds

An attempt is made to study theoretically the influence of an arbitrarily oriented quantizing magnetic field on the field emission from A II 3B V 2 compounds on the basis of a newly derived magneto-energy spectrum, based on k.p formalism, considering the anisotropies of the various band parameters. It is found, taking n-Cd 3As 2, as an example that the current density due to field emission under arbitrary magnetic quantization increases with increasing electron concentration in an oscillatory manner. Besides, the same current density increases with increasing electric field and decreasing magnetic field, respectively, in the magnetic quantum limit. In addition, the corresponding well-known results of parabolic energy bands are also obtained from the generalized expressions under limiting conditions.

The two-center Dalitz integral: Theory and algorithms for high precision computation

The general two-center Dalitz integral of the form: $$I_{if} = \frac{1}{{2\pi ^2 }}\smallint \frac{{dq}}{{q^2 }}\tilde \varphi _f^* (q - \alpha )\tilde \varphi _i (q - \beta )$$ is calculated analytically and numerically for an arbitrary set {i,f} of indices associated with the Fourier transforms\(\tilde \varphi _i (q + \beta )\) and\(\tilde \varphi _f (q - \alpha )\) of exponential-type orbitals. The analytical results for hydrogenic, Sturmian and other related functions, as well as for Slater-type orbitals with an arbitrary quantization axis, are presented as concise, closed expressions. These contain only a few finite summations of easily available quantities, such as Gaunt coefficients, Clausen hypergeometric polynomials of unit argument, spherical harmonics, etc. .... The present closed formulae are also valid for all scaling parameters of the orbitals involved. Furthermore, an additional angular momentum decomposition of the final result can readily be accomplished.

The debye screening length in degenerate n-Cd 3As 2 in the presence of an arbitrarily oriented quantizing magnetic field

The nature of the magnetic field dependence of the Debye screening length in degenerate n-Cd 3As 2 is shown to be oscillatory under the influence of arbitrary magnetic quantization.

Threshold extension in weighted PCM with arbitrary probability distribution and nonuniform quantization (Corresp.)

The threshold in the output signal-to-noise ratio (SNR) of weighted pulse-code modulation (PCM) is determined for an arbitrary probability distribution of the input signal and a logarithmic quantizer. Numerical results are given which show a reduction of 5.37 dB in the threshold, relative to classical PCM, for a nonuniform probability distribution and a logarithmic quantizer.

Quantization Complexity and Independent Measurements

It is known that, in general, the number of measurements in a pattern classification problem cannot be increased arbitrarily, when the class-conditional densities are not completely known and only a finite number of learning samples are available. Above a certain number of measurements, the performance starts deteriorating instead of improving steadily. It was earlier shown by one of the authors that an exception to this curse of finite sample is constituted by the case of binary independent measurements if a Bayesian approach is taken and uniform a priori on the unknown parameters are assumed. In this paper, the following generalizations are considered: arbitrary quantization and the use of maximum likelihood estimates. Further, the existence of an optimal quantization complexity is demonstrated, and its relationship to both the dimensionality of the measurement vector and the sample size are discussed. It is shown that the optimum number of quantization levels decreases with increasing dimensionality for a fixed sample size, and increases with the sample size for fixed dimensionality.