Fuzzy reasoning morphological operators and their optical implementation

Fuzzy-reasoning theory is widely used in industrial control. Mathematical morphology is a powerful tool to perform image processing. We apply fuzzy-reasoning theory to morphology and suggest a scheme of fuzzy-reasoning morphology, including fuzzy-reasoning dilation and erosion functions. These functions retain more fine details than the corresponding conventional morphological operators with the same structuring element. An optical implementation has been developed with area-coding and thresholding methods. (C) 1997 Optical Society of America.

Observing the fractional Fourier transform by free-space Fresnel diffraction

The fractional Fourier transform of an object can be observed in the free-space Fresnel diffraction pattern of the object. (C) 1997 Optical Society of America

Scaled fractional Fourier transform and its optical implementation

The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of phi and output scale. In addition, physically it relates the FRT with the general lens transform-the optical diffraction between two asymmetrically positioned planes before and after a lens. (C) 1997 Optical Society of America.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

Near-field hexagonal array illumination based on fractional Talbot effect

Hexagonal array is a basic structure widely exists in nature and adopted by optoclectronic device. A phase plate based on the fractional Talbot effect that converts a single expanded laser beam into a regular hexagonal array of uniformly illuminated apertures with virtually 100% efficiency is presented. The uniform hexagonal array illumination with a fill factor of 1/12 is demonstrated by the computer simulation. (C) 2006 Elsevier GmbH. All rights reserved.

Exact quantum master equation via the calculus on path integrals

An exact quantum master equation formalism is constructed for the efficient evaluation of quantum non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. A novel truncation scheme is further proposed and compared with other approaches to close the resulting hierarchically coupled equations of motion. The interplay between system-bath interaction strength, non-Markovian property, and required level of hierarchy is also demonstrated with the aid of simple spin-boson systems. (C) 2005 American Institute of Physics.

A Novel 0.72-6.2GHz Continuously-Tunable Delta Sigma Fractional-N Frequency Synthesizer

This paper presents a wideband Delta Sigma-based fractional-N synthesizer with three integrated quadrature VCOs for multiple-input multiple-output (MIMO) wireless communication applications. It continuously covers a wide range frequency from 0.72GHz to 6.2GHz that is suitable for multiple communication standards. The synthesizer is designed in 0.13-um RE CMOS process. The dual clock full differential multi-modulus divide (MMD) with low power consumption can operate over 9GHz under the worst condition. In the whole range frequency from 0.72GHz to 6.2GHz, the maximal tuning range of the QVCOs reaches 33.09% and their phase noise is -119d8/Hz similar to 124d8/Hz @1MHz. Its current is less than 12mA at a 1.2V voltage supply when it operates at the highest frequency of 6.2GHz.

An automata theoretic decision procedure for the propositional mu-calculus

The propositional mu-calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of Fischer and Ladner, the infinite looping construct of Streett, and the game logic of Parikh. We give an elementary time decision procedure, using a reduction to the emptiness problem for automata on infinite trees. A small model theorem is obtained as a corollary.