Symmetric Transfer Function Research Articles

Acousto-optic k-space filtering for multifrequency laser beam shaping

One of emerging applications of acousto-optic tunable filters (AOTFs) is spatial filtering of optical beams. A noncollinear AOTF has a tunable ring-shaped transfer function determined by geometry of the refractive index surface in a uniaxial crystal. We rigorously derive the geometrical parameters of the AOTF’s elliptic transfer function under noncritical phase matching condition in uniaxial crystals. This basic family of transfer functions can be used for synthesis of axially symmetric transfer functions with the help of multifrequency ultrasonic signals. A two-color tunable optical trap configuration is proposed based on a single AOTF used for laser beam shaping.

Parallel wave-based analog computing using metagratings.

Wave-based signal processing has witnessed a significant expansion of interest in a variety of science and engineering disciplines, as it provides new opportunities for achieving high-speed and low-power operations. Although flat optics desires integrable components to perform multiple missions, yet, the current wave-based computational metasurfaces can engineer only the spatial content of the input signal where the processed signal obeys the traditional version of Snell’s law. In this paper, we propose a multi-functional metagrating to modulate both spatial and angular properties of the input signal whereby both symmetric and asymmetric optical transfer functions are realized using high-order space harmonics. The performance of the designed compound metallic grating is validated through several investigations where closed-form expressions are suggested to extract the phase and amplitude information of the diffractive modes. Several illustrative examples are demonstrated to show that the proposed metagrating allows for simultaneous parallel analog computing tasks such as first- and second-order spatial differentiation through a single multichannel structured surface. It is anticipated that the designed platform brings a new twist to the field of optical signal processing and opens up large perspectives for simple integrated image processing systems.

Sonar signal representation mimicking the inner ear of horseshoe bats

Current models of the initial stages of auditory processing in mammals usually agree that the input signals are split into a bank of bandpass filters. However, the available models differ substantially in their level of complexity and the number of parameters needed. In the current work, the varying levels of complexity in filterbank models of the basilar membrane have been evaluated in the context of modeling the cochlear processing of natural biosonar echoes in horseshoe bats. To this end, three different types of filterbank models have been implemented to represent the range of complexity spanned by models that are in use for the human inner ear: The simplest model, a gammatone filterbank, is a linear model with symmetric filter transfer functions. The gammachirp filterbank is also linear, but mimics the asymmetric transfer functions of the basilar membrane. Finally, the dual resonance nonlinear (DRNL) model adds a level-dependent behavior. Here, all three models have been adapted to the specifics of the basilar membrane of horseshoe bats which is characterized by an “auditory fovea” with exceptionally high filter qualities. The outputs of the different models have been encoded into a sequence of neural spike times before being evaluated with various information-theoretic methods.

A binary symmetric based hybrid meta-heuristic method for solving mixed integer unit commitment problem integrating with significant plug-in electric vehicles

Conventional unit commitment is a mixed integer optimization problem and has long been a key issue for power system operators. The complexity of this problem has increased in recent years given the emergence of new participants such as large penetration of plug-in electric vehicles. In this paper, a new model is established for simultaneously considering the day-ahead hourly based power system scheduling and a significant number of plug-in electric vehicles charging and discharging behaviours. For solving the problem, a novel hybrid mixed coding meta-heuristic algorithm is proposed, where V-shape symmetric transfer functions based binary particle swarm optimization are employed. The impact of transfer functions utilised in binary optimization on solving unit commitment and plug-in electric vehicle integration are investigated in a 10 unit power system with 50,000 plug-in electric vehicles. In addition, two unidirectional modes including grid to vehicle and vehicle to grid, as well as a bi-directional mode combining plug-in electric vehicle charging and discharging are comparatively examined. The numerical results show that the novel symmetric transfer function based optimization algorithm demonstrates competitive performance in reducing the fossil fuel cost and increasing the scheduling flexibility of plug-in electric vehicles in three intelligent scheduling modes.

Model order reduction of second-order systems with nonlinear stiffness using Krylov subspace methods and their symmetric transfer functions

ABSTRACTIn this investigation, Model Order Reduction (MOR) of second-order systems having cubic nonlinearity in stiffness is developed for the first time using Krylov subspace methods and the associated symmetric transfer functions. In doing so, new second-order Krylov subspaces will be defined for MOR procedure which avoids the need to transform the second-order system to its state space form and thus the main characteristics of the second-order system such as symmetry and positive definiteness of mass and stiffness matrices will be preserved. To show the efficacy of the presented method, three examples will be considered as practical case studies. The first example is a nonlinear shear-beam building model subjected to a seismic disturbance. The second and third examples are nonlinear longitudinal vibration of a rod and vibration of a cantilever beam resting on a nonlinear elastic foundation, respectively. Simulation results in all cases show good accuracy of the vibrational response of the reduced order models when compared with the original ones while reducing the computational load.

Quantitative differential phase contrast imaging at high resolution with radially asymmetric illumination.

Half-circle illumination-based differential phase contrast (DPC) microscopy has been utilized to recover phase images through a pair of images along multiple axes. Recently, the half-circle based DPC using 12-axis measurements significantly provides a circularly symmetric phase transfer function to improve accuracy for more stable phase recovery. Instead of using half-circle-based DPC, we propose a new scheme of DPC under radially asymmetric illumination to achieve circularly symmetric phase transfer function and enhance the accuracy of phase recovery in a more stable and efficient fashion. We present the design, implementation, and experimental image data demonstrating the ability of our method to obtain quantitative phase images of microspheres, as well as live fibroblast cell samples.

Blind image quality assessment based on wavelet power spectrum in perceptual domain

Blind image quality assessment (BIQA) can assess the perceptual quality of a distorted image without a prior knowledge of its reference image or distortion type. In this paper, a novel BIQA model is developed in wavelet domain. Considering the multi-resolution and band-passing characteristics of discrete wavelet transform (DWT), an improvement over the power spectrum is put forward, i.e., dubbed wavelet power spectrum (WPS) estimation. Then, the concept of directional WPS is applied to simplify the calculation. Moreover, a rotationally symmetric modulation transfer function (MTF) of human visual system (HVS) is integrated as a filter, which makes the metric to be consistent with the human vision perception and more discriminative. Experiments are conducted on the LIVE databases and three other databases, and the results show that the proposed metric is highly correlated with subjective evaluations and it competes well with other state-of-the-art metrics in terms of effectiveness and robustness.

On the quadratic stability of switched linear systems associated with symmetric transfer function matrices

In this paper we give necessary and sufficient conditions for weak and strong quadratic stability of a class of switched linear systems consisting of two subsystems, associated with symmetric transfer function matrices. These conditions can simply be tested by checking the eigenvalues of the product of two subsystem matrices. This result is an extension of the result by Shorten and Narendra for strong quadratic stability, and the result by Shorten et al. on weak quadratic stability for switched linear systems. Examples are given to illustrate the usefulness of our results.

Some new results in the theory of negative imaginary systems with symmetric transfer matrix function

This note represents a first attempt to provide a definition and characterisation of negative imaginary systems for not necessarily rational transfer functions via a sign condition expressed in the entire domain of analyticity, along the same lines of the classic definition of positive real systems. Under the standing assumption of symmetric transfer functions, we then derive a necessary and sufficient condition that characterises negative imaginary transfer functions in terms of a matrix sign condition restricted to the imaginary axis, once again following the same line of argument of the standard positive real case. Using this definition, even transfer functions with a pole at the origin with double multiplicity, as well as with a possibly negative relative degree, can be negative imaginary.

Output Feedback Pole Assignment for Transfer Functions with Symmetries

This paper studies the problem of pole assignment for symmetric and Hamiltonian transfer functions. A necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given. Moreover, in the case where the McMillan degree coincides with the number of parameters appearing in the symmetric feedback transformations, we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains. The proof uses intersection theory in projective space as well as a formula for the degree of the complex Lagrangian Grassmann manifold.

Tangent spaces of rational matrix functions

We consider the task of determining tangent spaces for classes of rational matrix valued functions. Our analysis is based on methods from control theory, and in particular the theory of polynomial models. Explicit descriptions of tangent spaces of rational transfer functions, stable rational transfer functions, rational inner functions, and symmetric rational transfer functions are obtained. Moreover, a new proof of Delchamps's decomposition formula for the tangent bundle of rational transfer functions is given. A Riemannian metric as well as a symplectic structure is defined.

Tangent spaces of rational matrix functions

We consider the task of determining tangent spaces for classes of rational matrix valued functions. Our analysis is based on methods from control theory, and in particular the theory of polynomial models. Explicit descriptions of tangent spaces of rational transfer functions, stable rational transfer functions, rational inner functions, and symmetric rational transfer functions are obtained. Moreover, a new proof of Delchamps's decomposition formula for the tangent bundle of rational transfer functions is given. A Riemannian metric as well as a symplectic structure is defined.

Sampled-Data H2 Control for Symmetric Systems

This paper considers digital control problems for continuous-time systems having symmetric transfer functions. It is supposed that digital controllers are implemented with zero-order hold, discrete-time controller, and ideal or integral sampler. The following results are obtained : (1) stabilization : transfer functions of discretized systems with both types of samplers keep symmetries of original continuous-time transfer functions. A condition for discrete-time stabilizing controllers to be symmetric is obtained. (2) discrete-time H2 control synthesis : discrete-time H2 optimal controllers for symmetric discrete-time generalized plants are symmetric. (3) sampled-data H2 control synthesis : for symmetric continuous-time generalized plants with integral samplers, sampled-data H2 optimal controllers are symmetric, while symmetries can not be utilized with ideal samplers.

The uniqueness in designing multidimensional causal recursive digital filters possessing magnitude hyperspherical symmetry

It is shown that magnitude hyperspherically symmetric transfer functions of multidimensional (MD) causal recursive digital filters must have numerator and denominator polynomials that are separately magnitude hyperspherically symmetric. Further, the exact reference-domain magnitude hyperspherically symmetric denominator polynomial is of infinite order, possessing only one free parameter, and the magnitude hyperspherically symmetric numerator polynomial itself has to be a radial even function. The corresponding MD design problem is shown to be essentially a one-dimensional design problem. Filter transfer functions having good symmetry and moderate degree can be designed by using the presented procedure. >

Balanced realization of orthogonally symmetric transfer function matrices

Structural properties of minimal balanced realizations of orthogonally symmetric transfer function matrices are developed. These properties are then used to formulate a computationally efficient algorithm for determining balanced realizations of transfer function matrices in this class. The applicability of these realizations to circuit synthesis is indicated.

A note on cross Grammians for orthogonally symmetric realizations

The orthogonally symmetric property of realizations of orthogonally symmetric transfer function matrices is used to extend the result reported in [4]-[6] concerning cross Grammians of multiinput-multioutput systems. Two numerical examples are given to illustrate the generalization proposed here.

Minimal realization of a symmetric transfer-function matrix using expansion about a general point "a"

A procedure for the minimal realization of symmetric transfer function matrix by its expansion about an arbitrary point "a" is proposed. The procedure results in realizations leading to reciprocal network synthesis.

On a fundamental property of the cross- Gramian matrix

The cross-Gramian matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W_{c0} (T)</tex> for linear single-input single-output (SISO) dynamical systems has been related to the controllability and observability Gramians via <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W^{2}_{c0}(T)= W_{c}(T)W_{0}(T)</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T= \infty</tex> . The result is now proved for any arbitrary time interval <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> , and is extended to symmetric multivariable systems which have symmetric transfer function matrices.

On symmetric rational transfer functions

A detailed study of symmetric transfer functions is presented.

Minimal-order realizations for continuous-time two-power input-output maps

This paper considers two-power input-output maps which are continuous-time, impulsive, and time-invariant. Realizability, by a very general class of nonlinear differential systems, is characterized simply in terms of the symmetric Volterra transfer function. The characterization leads directly to a family of minimal-order realizations having the (feedforward) structure described by Crouch [6]. Members of the family have states which are related by quadratic homeomorphisms. An especially simple member of the family serves as a canonical form. The development is self-contained and unlike Crouch's requires only elementary mathematical tools.