Nanda Gopal

RICE: Rapid interconnect circuit evaluator

This paper describes RICE, an RLC interconnect evaluation tool based upon the moment-matching technique of Asymptotic Waveform Evaluation (AWE). The RLC circuit moments are calculated by a path-tracing algorithm which enables the analysis of large interconnect models several thousand times faster than a circuit simulation while requiring 5 to 10 times less memory. RICE also includes a new approach for determining the circuit dominant time-constants which avoids the inherent instability problems associated with moment matching methods in general.

Localized measurement of emergent image frequencies by Gabor wavelets

The authors derive, implement, and demonstrate a computational approach for the measurement of emergent image frequencies. Measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space, conflicting requirements that are shown to be balanced by a generalized uncertainty relationship. Such spectral measurements can be obtained from the responses of multiple wavelet-like channel filters that sample the signal spectrum, and that yield a locus of possible solutions for each locally emergent frequency. It is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are Gabor wavelets. A constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal. The measurement of frequencies is then cast as an ill-posed extremum problem regularized by the stabilizing term, leading to an iterative constraint propagation algorithm. The technique is demonstrated by application to a variety of 2-D textured images. >

Time-domain macromodels for VLSI interconnect analysis

This paper presents a method of obtaining time-domain macromodels of VLSI interconnection networks for circuit simulation. The goal of this work is to include interconnect parasitics in a circuit simulation as efficiently as possible, without significantly compromising accuracy. Stability issues and enhancements to incorporate transmission line interconnects are also discussed. A unified circuit simulation framework, incorporating different classes of interconnects and based on the proposed macromodels, is described. The simplicity and generality of the macromodels is demonstrated through examples employing RC- and RLC-interconnects. >

On the stability of moment-matching approximations in asymptotic waveform evaluation

Asymptotic waveform evaluation (AWE), which is based upon moment-matching, has been demonstrated as an efficient approach for CAD circuit simulation/analysis. The authors describe an approach for overcoming the inherent instability associated with AWE and moment-matching methods as they apply to circuit analysis problems. The efficiency and accuracy of this algorithm were demonstrated in the analysis of large, lumped RLC interconnect-circuit analysis problems and printed circuit board interconnections.<<ETX>>

Enhancing the stability of asymptotic waveform evaluation for digital interconnect circuit applications

Asymptotic Waveform Evaluation (AWE) has been demonstrated as an efficient approach for interconnect circuit simulation/analysis. However, since it is based upon moment-matching, it is prone to yielding unstable approximations for stable circuits. This paper describes a systematic approach for alleviating the inherent instability associated with AWE and moment-matching methods as they apply to passive, digital, interconnect circuits. The efficiency and accuracy of this approach are demonstrated on several large, RLC interconnect-circuit problems. >

AWE macromodels of VLSI interconnect for circuit simulation

The results of linear asymptotic waveform evaluation (AWE) and of nonlinear circuit simulation are combined for the purpose of efficiently incorporating accurate interconnect information in the overall circuit description. A simple macromodel based on the y-parameter description of a complex interconnect network is discussed. The model makes possible the reduction of large, stiff interconnect configurations into compact representations that pose minimal problems to conventional circuit simulation techniques. The macromodel can be incorporated directly into a conventional circuit simulation with no modification of the original simulation software. The techniques are suitable for development as a software library that can be used to enhance existing simulators so that they can handle large VLSI interconnect configurations very efficiently. In addition, the ability to handle elements at the port level makes approach extremely attractive for any linear(ized) macromodels or for application such as mixed-mode simulation.<<ETX>>

Numerical Analysis of Image Patterns

We find similarities between spatial pattern analysis and other low-level cooperative visual processes. Numerical algorithms for computing intrinsic scene attributes, e.g. shape-from-X (shading, texture, etc.) and optical flow typically involve estimating generalized orientation components via iterative constraint propagation. Smoothing or regularizing terms imposed on the constraint equations often enhance the uniqueness / stability (well-posedness) of the solutions. The numerical approach to visual pattern analysis developed here proceeds analogously via estimation of emergent 2-D image frequencies. Unlike shape-from-X or optical flow paradigms, constraints are derived from the responses of multiple oriented spatial frequency channels rather than directly from the image irradiance measurements. By using channel filters that are sufficiently concentrated in both space and frequency, highly accurate spatial frequency estimates are computed on a local basis. Two methods are proposed. In the first, constrained estimates of the emergent image frequencies are obtained by resolving the responses of multiple channel filters in a process similar to photometric stereo. The second approach formulates the estimation of frequencies as an extremum problem regularized by a smoothing term. An iterative constraint propagation algorithm is developed analogous to those used in variational / relaxational approaches to shape-from-X (shading, texture) and optical flow. Examples illustrate each approach using synthetic and natural images.

Channel interactions in visible pattern analysis

The efficacy of the 2-D Gabor channel filters for segmenting images based on the division of the image into textures was established previously. In the present work, the authors extend the model for the direct estimation of the emergent spatially localized orientation/frequencies of visible patterns using a variational scheme. The most significant result of this extension is that patterns with space-varying frequency characteristics, arising from, e.g. surface deformation, can still be analyzed and segregated. Moreover, the information extracted can provide a means for developing shape-from-texture algorithms that are optimally localized. The implementation of the filtering scheme is described.<<ETX>>

Multiple channel surface orientation from texture

This paper studies the computation of surface orientation by analyzing the responses of multiple spatio-spectrally localized channel filters. Images containing textures that encode information about local surface orientation are decomposed into narrowband sub-images possessing characteristic radial frequency and orientation properties. By analyzing the spatial variation in the filter responses, information about the spatial variation in the pattern I texture can be elucidated and subsequently used to estimate surface orientation. The channel filters used are Gaborfunctions, which have previously been applied successfully to related problems in texture analysis, segmentation, and characterization. The Gabor functions are plausible approximations to the responses of the highly oriented simple cells in mammalian striate cortex. They also possess important properties for the local isolation and characterization of textures. In our approach, texture gradients are modeled as giving rise to pattern frequency gradients that can be exiracted on a highly localized basis. A variational optimization procedure for estimating the pattern frequency variation is implemented via a discrete relaxation procedure that is suitable for a massively parallel computation. The result of the optimization procedure is a stable dense map describing the localized image frequency content. The computed image frequency characteristics are then used to define a texture density measure used in a planar-surface approximation procedure, yielding slant/tilt estimates describing the surface orientation. Experimental results support the theoretical derivations.

Numerical analysis of visual patterns

Summary form only given, as follows. Similarities are found between spatial pattern analysis and other low-level cooperative image analysis tasks. Visual pattern analysis proceeds analogously via estimation of emergent 2D image frequencies. Unlike shape-from-X or optical flow paradigms, constraints are derived from the responses of multiple oriented spatial frequency channels rather than directly from the image irradiance measurements. By selecting channel filters that are sufficiently concentrated in both space and frequency, highly accurate spatial frequency estimates are computed on a local basis. Two related methods are proposed. In the first, a constrained estimate of the emergent image frequencies is obtained by resolving the responses of multiple channel filters in a process similar to photometric stereo. The second approach formulates the estimation of frequencies as an extremum problem regularized by a smoothing term. An iterative constraint propagation algorithm is developed analogous to those used in variational/relaxational approaches to shape-from-X (shading, texture) and optical flow. Examples illustrate both approaches using synthetic and natural images.<<ETX>>