Ngai Wong

A generalized direct-form delta operator-based IIR filter with minimum noise gain and sensitivity

This brief presents the derivation of an arbitrary order delta operator-based direct-form IIR filter with minimum roundoff noise gain and sensitivity. It utilizes the concept of different coupling coefficients at different branch nodes for better noise gain suppression. Two possible structures for realizing the inverse delta operator are considered and procedures for calculating the optimal filter coefficients are given. By means of state-space representation and matrix manipulation, it is also shown that expressions for sensitivity measures of different filter coefficients and their corresponding roundoff noise gain expressions are the same. This enables the simultaneous minimization of sensitivity and noise power for the proposed generalized filter structure.

Level-set-based inverse lithography for photomask synthesis

Inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem. We show how the inverse lithography problem can be addressed as an obstacle reconstruction problem or an extended nonlinear image restoration problem, and then solved by a level set time-dependent model with finite difference schemes. We present explicit detailed formulation of the problem together with the first-order temporal and second-order spatial accurate discretization scheme. Experimental results show the superiority of the proposed level set-based ILT over the mainstream gradient methods.

Robust level-set-based inverse lithography

Level-set based inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem, interpreted with a time-dependent model, and then solved as a partial differential equation with finite difference schemes. This paper focuses on developing level-set based ILT for partially coherent systems, and upon that an expectation-orient optimization framework weighting the cost function by random process condition variables. These include defocus and aberration to enhance robustness of layout patterns against process variations. Results demonstrating the benefits of defocus-aberration-aware level-set based ILT are presented.

IIR Approximation of FIR Filters Via Discrete-Time Vector Fitting

We present a novel technique for approximating finite-impulse-response (FIR) filters with infinite-impulse-response (IIR) structures through extending the vector fitting (VF) algorithm, used extensively for continuous-time frequency-domain rational approximation, to its discrete-time counterpart called VFz. VFz directly computes the candidate filter poles and iteratively relocates them for progressively better approximation. Each VFz iteration consists of the solutions of an overdetermined linear equation and an eigenvalue problem, with real-domain arithmetic to accommodate complex poles. Pole flipping and maximum pole radius constraint guarantee stability and robustness against finite-precision implementation. Comparison against existing algorithms confirms that VFz generally exhibits fast convergence and produces highly accurate IIR approximants.

An efficient algorithm for downconverting multiple bandpass signals using bandpass sampling

Bandpass sampling is a useful alternative for direct digital downconversion in software radio. It significantly relaxes the analog-to-digital converter (ADC) sampling rate requirement and facilitates the design goal of moving the ADC as close as possible to the antenna. This paper presents a modified interpretation to the graph of allowable sampling frequencies in uniform bandpass sampling. It is shown that the position and guard bands of a downconverted bandpass signal band are highly related to the order of the valid sampling range, called the wedge order. An efficient algorithm is then proposed, which significantly reduces the computational load in determining the valid sampling frequencies to downconvert multiple distinct bandpass signals. Conditions for the placement of bandpass signals to utilize a given sampled bandwidth are also discussed.

MFTI: matrix-format tangential interpolation for modeling multi-port systems

Numerous algorithms to macromodel a linear time-invariant (LTI) system from its frequency-domain sampling data have been proposed in recent years [1,2,3,4,5,6,7,8], among which Loewner matrix-based tangential interpolation proves to be especially suitable for modeling massive-port systems [6, 7,8]. However, the existing Loewner matrix-based method follows vector-format tangential interpolation (VFTI), which fails to explore all the information contained in the frequency samples. In this paper, a novel matrix-format tangential interpolation (MFTI) is proposed, which requires much fewer samples to recover the system and yields better accuracy when handling under-sampled, noisy and/or ill-conditioned data. A recursive version of MFTI is proposed to further reduce the computational complexity. Numerical examples then confirm the superiority of MFTI over VFTI.

An Efficient Projector-Based Passivity Test for Descriptor Systems

An efficient passivity test based on canonical projector techniques is proposed for descriptor systems (DSs) widely encountered in circuit and system modeling. The test features a natural flow that first evaluates the index of a DS, followed by possible decoupling into its proper and improper subsystems. Explicit state-space formulations for respective subsystems are derived to facilitate further processing such as model order reduction and/or passivity enforcement. Efficient projector construction and a fast generalized Hamiltonian test for the proper-part passivity are also elaborated. Numerical examples then confirm the superiority of the proposed method over existing passivity tests for DSs based on linear matrix inequalities or skew-Hamiltonian/Hamiltonian matrix pencils.

GHM: a generalized Hamiltonian method for passivity test of impedance/admittance descriptor systems

A generalized Hamiltonian method (GHM) is proposed for passivity test of descriptor systems (DSs) which describe impedance or admittance input-output responses. GHM can test passivity of DSs with any system index without minimal realization. This frequency-independent method can avoid the time-consuming system decomposition as required in many existing DS passivity test approaches. Furthermore, GHM can test systems with singular D + DT where traditional Hamiltonian method fails, and enjoys a more accurate passivity violation identification compared to frequency sweeping techniques. Numerical results have verified the effectiveness of GHM. The proposed method constitutes a versatile tool to speed up passivity check and enforcement of DSs and subsequently ensures globally stable simulations of electrical circuits and components.

Global optimization of common subexpressions for multiplierless synthesis of multiple constant multiplications

In the context of multiple constant multiplication (MCM) design, we propose a novel common subexpression elimination (CSE) algorithm that models the optimal synthesis of coefficients into a 0-1 mixed-integer linear programming (MILP) problem. A time delay constraint is included for synthesis. We also propose coefficient decompositions that combine all minimal signed digit (MSD) representations and the shifted sum (difference) of coefficients. In the examples we demonstrate, the proposed solution space further reduces the number of adders/subtractors in the MCM synthesis.

Roundoff noise minimization in a modified direct-form delta operator IIR structure

Among various direct-form delta operator realized filter structures, the delta transposed direct-form II (/spl delta/DFIIt) has been shown to produce the lowest roundoff noise gain in finite wordlength implementations. Recent analyses focus on the optimization of the free parameter /spl Delta/ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified /spl delta/DFIIt second-order section in which the /spl Delta/s and filter coefficients at different branches are separately scaled to achieve improved roundoff noise gain minimization. Expressions for the filter coefficients are derived, and reduction of roundoff noise gain is verified by numerical examples.