This paper gives an overview of scale-space and image enhancement techniques which are based on p... more This paper gives an overview of scale-space and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate a-priori knowledge into the evolution. We sketch basic ideas behind the different filter models, discuss their theoretical foundations and scale-space properties, discrete aspects, suitable algorithms, generalizations, and applications.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Jan 1, 1996
We present a new synthesis strategy that can automate fully the path from an analog circuit topol... more We present a new synthesis strategy that can automate fully the path from an analog circuit topology and performance specifications to a sized circuit schematic. This strategy relies on asymptotic waveform evaluation to predict circuit performance and simulated annealing to solve a novel unconstrained optimization formulation of the circuit synthesis problem. We have implemented this strategy in a pair of tools called ASTRX and OBLX. To show the generality of our new approach, we have used this system to resynthesize essentially all the analog synthesis benchmarks published in the past decade; ASTRX/OBLX has resynthesized circuits in an afternoon that, for some prior approaches, had required months. To show the viability of the approach on difficult circuits, we have resynthesized a recently published (and patented), high-performance operational amplifier; ASTRX/OBLX achieved performance comparable to the expert manual design. And finally, to test the limits of the approach on industrial-sized problems, we have synthesized the component cells of a pipelined A/D converter; ASTRX/OBLX successfully generated cells 2-3× more complex than those published previously
A hybrid system is modeled with a finite set of locations and a differential inclusion associated... more A hybrid system is modeled with a finite set of locations and a differential inclusion associated with each location. We discuss a subclass of hybrid systems with constant rectangular differential inclusions. The continuous state of the system is x ∃ IRn with x i evolving with differential inclusion x i [L i , U i ] where L i , U i are integers (i.e., the slope of trajectory of x i could be changing, but is restricted to remain within [L i , U i ]). A transition from one location to another can be made provided the state satisfies the enabling condition for the transition. The state can also be initialized to a new value during the transition. The differential inclusion for x i can be changed when x i is an integer or when x i is initialized to a new value. We show that the verification problem for this class of hybrid systems is decidable. With this approach, systems with unsynchronized and drifting clocks can be modeled, a general differential equation can be abstracted by breaking the state space into regions with constant differential inclusions, and many previously presented hybrid system examples can be verified.
IEEE Transactions on Information Theory, Jan 1, 1998
In this paper we review some recent interactions between harmonic analysis and data compression. ... more In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon's R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed by block coding gives an optimal lossy compression technique; practical developments like transform-based image compression have been inspired by this result. In this paper we also discuss connections perhaps less familiar to the information theory community, growing out of the field of harmonic analysis. Recent harmonic analysis constructions, such as wavelet transforms and Gabor transforms, are essentially optimal transforms for transform coding in certain settings. Some of these transforms are under consideration for future compression standards. We discuss some of the lessons of harmonic analysis in this century. Typically, the problems and achievements of this field have involved goals that were not obviously related to practical data compression, and have used a language not immediately accessible to outsiders. Nevertheless, through an extensive generalization of what Shannon called the “sampling theorem”, harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations. We explain why harmonic analysis has interacted with data compression, and we describe some interesting recent ideas in the field that may affect data compression in the future
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Jan 1, 1997
The performance of high-speed electronic systems is limited by interconnect-related failure modes... more The performance of high-speed electronic systems is limited by interconnect-related failure modes such as coupled noise. We propose new techniques for alleviating the problems caused by coupling between signal lines on integrated circuits. We show that models used by previous work on coupled noise-constrained layout synthesis do not allow the use of several important degrees of freedom. These degrees of freedom include the ability to utilize dynamic noise margins rather than static noise margins, the dependence of coupled noise on drive strength, and the possibility of using overlaps to reduce susceptibility to noise. We derive an expression for the coupled noise integral and a bound for the peak coupled noise voltage which shows order of magnitude improvements in both accuracy and fidelity compared to the charge sharing model used in previous work. We use the new bounds to guide a greedy channel router, which manipulates exact adjacency information at every stage, allowing it to introduce jogs or doglegs when necessary for coupled noise reduction. Experimental results indicate that our algorithm compares favorably to previous work. The coupled noise is significantly reduced on benchmark instances.
Impression of an external signal upon an oscillator of similar fundamental frequency affects both... more Impression of an external signal upon an oscillator of similar fundamental frequency affects both the instantaneous amplitude and instantaneous frequency. Using the assumption that time constants in the oscillator circuit are small compared to the length of one beat cycle, a differential equation is derived which gives the oscillator phase as a function of time. With the aid of this equation, the transient process of "pull-in" as well as the production of a distorted beat note are described in detail. It is shown that the same equation serves to describe the motion of a pendulum suspended in a viscous fluid inside a rotating container. The whole range of locking phenomena is illustrated with the aid of this simple mechanical model.
Impression of an external signal upon an oscillator of similar fundamental frequency affects both... more Impression of an external signal upon an oscillator of similar fundamental frequency affects both the instantaneous amplitude and instantaneous frequency. Using the assumption that time constants in the oscillator circuit are small compared to the length of one beat cycle, a differential equation is derived which gives the oscillator phase as a function of time. With the aid of this equation, the transient process of "pull-in" as well as the production of a distorted beat note are described in detail. It is shown that the same equation serves to describe the motion of a pendulum suspended in a viscous fluid inside a rotating container. The whole range of locking phenomena is illustrated with the aid of this simple mechanical model.
This paper gives an overview of scale-space and image enhancement techniques which are based on p... more This paper gives an overview of scale-space and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate a-priori knowledge into the evolution. We sketch basic ideas behind the different filter models, discuss their theoretical foundations and scale-space properties, discrete aspects, suitable algorithms, generalizations, and applications.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Jan 1, 1996
We present a new synthesis strategy that can automate fully the path from an analog circuit topol... more We present a new synthesis strategy that can automate fully the path from an analog circuit topology and performance specifications to a sized circuit schematic. This strategy relies on asymptotic waveform evaluation to predict circuit performance and simulated annealing to solve a novel unconstrained optimization formulation of the circuit synthesis problem. We have implemented this strategy in a pair of tools called ASTRX and OBLX. To show the generality of our new approach, we have used this system to resynthesize essentially all the analog synthesis benchmarks published in the past decade; ASTRX/OBLX has resynthesized circuits in an afternoon that, for some prior approaches, had required months. To show the viability of the approach on difficult circuits, we have resynthesized a recently published (and patented), high-performance operational amplifier; ASTRX/OBLX achieved performance comparable to the expert manual design. And finally, to test the limits of the approach on industrial-sized problems, we have synthesized the component cells of a pipelined A/D converter; ASTRX/OBLX successfully generated cells 2-3× more complex than those published previously
A hybrid system is modeled with a finite set of locations and a differential inclusion associated... more A hybrid system is modeled with a finite set of locations and a differential inclusion associated with each location. We discuss a subclass of hybrid systems with constant rectangular differential inclusions. The continuous state of the system is x ∃ IRn with x i evolving with differential inclusion x i [L i , U i ] where L i , U i are integers (i.e., the slope of trajectory of x i could be changing, but is restricted to remain within [L i , U i ]). A transition from one location to another can be made provided the state satisfies the enabling condition for the transition. The state can also be initialized to a new value during the transition. The differential inclusion for x i can be changed when x i is an integer or when x i is initialized to a new value. We show that the verification problem for this class of hybrid systems is decidable. With this approach, systems with unsynchronized and drifting clocks can be modeled, a general differential equation can be abstracted by breaking the state space into regions with constant differential inclusions, and many previously presented hybrid system examples can be verified.
IEEE Transactions on Information Theory, Jan 1, 1998
In this paper we review some recent interactions between harmonic analysis and data compression. ... more In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon's R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed by block coding gives an optimal lossy compression technique; practical developments like transform-based image compression have been inspired by this result. In this paper we also discuss connections perhaps less familiar to the information theory community, growing out of the field of harmonic analysis. Recent harmonic analysis constructions, such as wavelet transforms and Gabor transforms, are essentially optimal transforms for transform coding in certain settings. Some of these transforms are under consideration for future compression standards. We discuss some of the lessons of harmonic analysis in this century. Typically, the problems and achievements of this field have involved goals that were not obviously related to practical data compression, and have used a language not immediately accessible to outsiders. Nevertheless, through an extensive generalization of what Shannon called the “sampling theorem”, harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations. We explain why harmonic analysis has interacted with data compression, and we describe some interesting recent ideas in the field that may affect data compression in the future
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Jan 1, 1997
The performance of high-speed electronic systems is limited by interconnect-related failure modes... more The performance of high-speed electronic systems is limited by interconnect-related failure modes such as coupled noise. We propose new techniques for alleviating the problems caused by coupling between signal lines on integrated circuits. We show that models used by previous work on coupled noise-constrained layout synthesis do not allow the use of several important degrees of freedom. These degrees of freedom include the ability to utilize dynamic noise margins rather than static noise margins, the dependence of coupled noise on drive strength, and the possibility of using overlaps to reduce susceptibility to noise. We derive an expression for the coupled noise integral and a bound for the peak coupled noise voltage which shows order of magnitude improvements in both accuracy and fidelity compared to the charge sharing model used in previous work. We use the new bounds to guide a greedy channel router, which manipulates exact adjacency information at every stage, allowing it to introduce jogs or doglegs when necessary for coupled noise reduction. Experimental results indicate that our algorithm compares favorably to previous work. The coupled noise is significantly reduced on benchmark instances.
Impression of an external signal upon an oscillator of similar fundamental frequency affects both... more Impression of an external signal upon an oscillator of similar fundamental frequency affects both the instantaneous amplitude and instantaneous frequency. Using the assumption that time constants in the oscillator circuit are small compared to the length of one beat cycle, a differential equation is derived which gives the oscillator phase as a function of time. With the aid of this equation, the transient process of "pull-in" as well as the production of a distorted beat note are described in detail. It is shown that the same equation serves to describe the motion of a pendulum suspended in a viscous fluid inside a rotating container. The whole range of locking phenomena is illustrated with the aid of this simple mechanical model.
Impression of an external signal upon an oscillator of similar fundamental frequency affects both... more Impression of an external signal upon an oscillator of similar fundamental frequency affects both the instantaneous amplitude and instantaneous frequency. Using the assumption that time constants in the oscillator circuit are small compared to the length of one beat cycle, a differential equation is derived which gives the oscillator phase as a function of time. With the aid of this equation, the transient process of "pull-in" as well as the production of a distorted beat note are described in detail. It is shown that the same equation serves to describe the motion of a pendulum suspended in a viscous fluid inside a rotating container. The whole range of locking phenomena is illustrated with the aid of this simple mechanical model.
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