Showing papers in "IEEE Transactions on Circuits and Systems in 1986"

Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit

Abstract: We describe how several optimization problems can be rapidly solved by highly interconnected networks of simple analog processors. Analog-to-digital (A/D) conversion was considered as a simple optimization problem, and an A/D converter of novel architecture was designed. A/D conversion is a simple example of a more general class of signal-decision problems which we show could also be solved by appropriately constructed networks. Circuits to solve these problems were designed using general principles which result from an understanding of the basic collective computational properties of a specific class of analog-processor networks. We also show that a network which solves linear programming problems can be understood from the same concepts.

The double scroll family

Abstract: This paper provides a rigorous mathematical proof that the double scroll is indeed chaotic. Our approach is to derive a linearly equivalent class of piecewise-linear differential equations which includes the double scroll as a special case. A necessary and sufficient condition for two such piecewise-linear vector fields to be linearly equivalent is that their respective eigenvalues be a scaled version of each other. In the special case where they are identical, we have exact equivalence in the sense of linear conjugacy. An explicit normalform equation in the context of global bifurcation is derived and parametrized by their eigenvalues. Analytical expressions for various Poincare maps are then derived and used to characterize the birth and the death of the double scroll, as well as to derive an approximate one-dimensional map in analytic form which is useful for further bifurcation analysis. In particular, the analytical expressions characterizing various half-return maps associated with the Poincare map are used in a crucial way to prove the existence of a Shilnikov-type homoclinic orbit, thereby establishing rigorously the chaotic nature of the double scroll. These analytical expressions are also fundamental in our in-depth analysis of the birth (onset of the double scroll) and death (extinction of chaos) of the double scroll. The unifying theme throughout this paper is to analyze the double scroll system as an unfolding of a large family of piecewise-linear vector fields in R^3 . Using this approach, we were able to prove that the chaotic dynamics of the double scroll is quite common, and is robust because the associated horseshoes predicted from Shilnikov's theorem are structurally stable. In fact, it is exhibited by a large family (in fact, infinitely many linearlyequivalent circuits) of vector fields whose associated piecewise-linear differential equations bear no resemblance to each other. It is therefore remarkable that the normalized eigenvalues, which is a local concept, completely determine the system's global qualitative behavior.

Frequency-response masking approach for the synthesis of sharp linear phase digital filters

Abstract: If each delay element of a linear phase low-pass digital filter is replaced by M delay elements, an (M + 1) -band filter is produced. The transition-width of this (M + 1) -band filter is 1/M that of the prototype low-pass filter. A complementary filter can be obtained by subtracting the output of the (M + 1) -band filter from a suitably delayed version of the input. The complementary filter is an (M + 1) -band filter whose passbands and stopbands are the stopbands and passbands, respectively, of the original (M + 1) -band filter. If the frequency responses of the original ( M + 1) -band filter and its complementary filter are properly masked and recombined, narrow transition-band filter can be obtained. This technique can be used to design sharp low-pass, high-pass, bandpass, and bandstop filters with arbitrary passband bandwidth.

Multitone signals with low crest factor

Abstract: Using some results from the recent mathematics literature, we show how to generate signals with perfect low-pass or bandpass spectra which have very low crest factors (under 6 dB). An application to multitone frequency response testing is given.

Hyper chaos: Laboratory experiment and numerical confirmation

Abstract: Hyperchaos has been observed, for the first time, from a real physical system: a very simple fourth-order electrical circuit. It is autonomous and reciprocal and has only one nonlinear element, a three-segment piecewise-linear resistor. Because of the circuit's simplicity, the laboratory measurements have been confirmed by digital computer simulations. The hyperchaotic nature is confirmed by the two positive Lyapunov exponents associated with the attractor, which is a fractal with a Lyapunov dimension between 3 and 4.

Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse

Abstract: This paper presents an analysis of static stability in electric power systems. The study is based on a model consisting of the classical swing equation characterization for generators and constant admittance, PV bus and/or PQ bus load representations which, in general, leads to a semi-explicit (or constrained) system of differential equations. A precise definition of static stability is given and basic concepts of static bifurcation theory are used to show that this definition does include conventional notions of steady-state stability and voltage collapse, but it provides a basis for rigorous analysis. Static bifurcations of the load flow equations are analyzed using the Liapunov-Schmidt reduction and Taylor series expansion of the resulting reduced bifurcation equation. These procedures have been implemented using symbolic computation (in MASYMA). It is shown that static bifurcations of the load flow equations are associated with either divergence-type instability or loss of causality. Causality issues are found to be an important factor in understanding voltage collapse and play a central role in organizing global power system dynamics when loads other than constant admittance are present.

Stability and the matrix Lyapunov equation for discrete 2-dimensional systems

Abstract: The stability of two-dimensional, linear, discrete systems is examined using the 2-D matrix Lyapunov equation. While the existence of a positive definite solution pair to the 2-D Lyapunov equation is sufficient for stability, the paper proves that such existence is not necessary for stability, disproving a long-standing conjecture.

Novel MOS resistive circuit for synthesis of fully integrated continuous-time filters

Abstract: This paper describes a new MOS resistive circuit containing four matched MOS transistors. It allows to fully integrate known active RC filter structures on a single chip without externals components. Integrator, summer and lossy integrator circuits with a single operational amplifier are shown. The new circuits improve on previously suggested MOS active filters.

On the sensitivity of linear state-space systems

Abstract: This paper contains new measures to describe the transfer function sensitivity of state-space systems with respect to value and parameter perturbations. These measures are related to the newly defined generalized Gramian matrices. The value respecting the parameter variations contains the sensitivity at discrete frequency points, pole and zero sensitivities and the integral sensitivity as special cases. A general relation to the variance of the weighted output noise can be obtained in the case of a perturbed realization which is l_2 -scaled under a general non-white input process. The complete class of representations with minimum sensitivity and noise is given. The corresponding necessary and sufficient conditions lead to an analytic design of optimal state-space systems.

Canonical piecewise-linear modeling

Abstract: To take advantage of the remarkable computational efficiency of the canonical piecewise-linear approach for dc nonlinear electronic circuit analysis, the devices must be modeled by a canonical piecewise-linear model. This paper presents a unified parameter optimization algorithm for constructing such models. This algorithm is then applied to derive prototype canonical piecewise-linear models of p-n junction diodes, bipolar transistors, MOSFET's, and GaAs FET's. The canonical piecewise-linear model can be regarded as a universal model since its form remains unchanged for all devices. Only the coefficients differ from one device to another. For large-scale circuits, the canonical piecewise-linear representation has a decisive advantage over other representations in regard to the number of memory locations needed to specify the equations.

A new adaptive IIR filter

Abstract: A family of stochastic approximation variants of the Steiglitz-McBride identification scheme [1]-[3] is developed for adaptive IIR filtering. Parameter convergence is shown by computer simulation. An interesting phenomenon, global convergence regardless of local minima, is observed.

Design of almost minimax FIR filters in one and two dimensions by WLS techniques

Abstract: The design of Finite Impulse Response (FIR) filters in one or several dimensions can be performed with good computational efficiency using a Weighted Least Square (WLS) design. Minimax design, which is often preferred, is computationally burdensome, principally in two dimensions. This paper draws attention to the design of minimax filters using iterative WLS techniques for one-dimensional filters and extends the approach to two-dimensional filters. For two dimensions the techniques apply to both rectangular and hexagonal sampling grids. Examples demonstrate flexibility and good computational efficiency. The paper also illustrates a promising new approach to filter design which couples the very general WLS methodology to the less manageable but often preferred minimax performance criterion.

Adaptive filters with individual adaptation of parameters

Abstract: Conventional gradient-type adaptive filters use the fixed convergence factor \mu which is normally chosen to be the same for all the filter parameters. In this paper, we propose to use individual convergence factors which are optimally tailored to adapt individual filter parameters. Furthermore, we propose to adjust the individual convergence factors in real time so that their values are kept optimum for a new set of input variables. We call this approach "individual" adaptation as opposed to the conventional fixed "group" adaptation using the same fixed \mu for all the filter parameters. Computer simulation results show that the individual adaptation approach yields much better filters than the conventional fixed group adaptation approach. Optimization of individual time-varying convergence factors leads to a constraint which may be satisfied by several different algorithms. We propose and investigate here two algorithms satisfying the above constraint: individual adaptation (IA) and homogeneous adaptation (HA). The HA algorithm turns out to have the general form as some well known gradient algorithms that normalize the step size which were previously obtained either intuitively or using involved derivations. Both IA and HA are shown to provide much better performance than the conventional "group" adaptation. However, for several simulations, IA provides better performance than HA, at the expense of increased computation.

A high-frequency CMOS linear transconductance element

Abstract: A simple four-transistor, linear, tunable, high-frequency transconductance element is described. By using a pair of composite n -channel- p -channel devices, the circuit achieves its linearity by current differencing without undue matching requirements. It is shown that linearity and frequency response can be optimized simultaneously by appropriate choice of device dimensions. The performance is verified by SPICE simulations, and an operational transconductance amplifier (OTA) is used as one example for the many applications of the proposed element.

Flowgraph analysis of large electronic networks

Abstract: The paper presents a new method for signal flowgraph analysis of large electronic networks. A hierarchical decomposition approach is realized using the so-called upward analysis of the decomposed network. This approach allows fully symbolic network formulas to be obtained in time linearly proportional to the size of the network. A multiconnection characterization, suitable for upward analysis, has been defined and used in topological formulas. Examples of large scale networks analysis are discussed. The approach can be used to obtain symbolic solutions of linear systems of equations.

Continuous-time MOSFET-C filters in VLSI

Abstract: The desirable features of fully integrated, VLSI-compatible continuous-time filters are discussed. A recently proposed integrated continuous-time filtering technique is reviewed, in which MOS transistors are used in place of resistors along with nonlinearity cancellation and on-chip automatic tuning. The filters obtained using this technique are compared to switched-capacitor (SC) filters, digital filters, and continuous-time filters using different techniques. Representative experimental results are given, demonstrating the high performance that can be achieved.

Modification of Banu - Tsividis continuous-time integrator structure

Abstract: Addition of a matched pair of MOS transistors is proposed as a modification to the Banu-Tsividis fully balanced integrator structure [1]. Its application allows a high linearity of the balanced integrator to be obtained. Additionally, its transfer function does not depend on the threshold voltage V_T , and it minimizes temperature and body effects.

Dynamic testing and diagnostics of A/D converters

Abstract: A method is derived to measure the integral and differential nonlinearity of an ADC using a sinewave with unknown amplitude and offset. The uncertainty of the measurement is also estimated. In a second phase, the integral nonlinearity is analyzed, using Walsh Transforms, to identify the nonlinearity at the bit level of the ADC.

Van der Pol and chaos

Abstract: Experimental confirmation has been made on a driven relaxation oscillator circuit, first presented by Van der Pol, of the periodadding route to chaos. The nonlinear element in the circuit is a neon bulb, modeled by a three-segment piecewise-linear current-controlled resistor. A simple nonlinear circuit model has been used to reproduce in simulations the experimentally-observed period-adding phenomenon.

Synthesis of 2-D separable denominator digital filters with minimum roundoff noise and no overflow oscillations

Abstract: This paper presents a new expression of the variance of roundoff noise in 2-D separable denominator digital filters described by Roesser's local state-space model. The covariance matrices and noise matrices necessary to analyze the variance of roundoff noise under the 1_2 norm scaling are obtained as the solutions of Liapunov equations. The synthesis problem of 2-D separable denominator digital filters with minimum roundoff noise are formulated under the 1_2 norm scaling. The synthesis method of 2-D minimum noise realizations under the 1_2 norm scaling is proposed by applying the minimization technique of roundoff noise in the 1-D case. Furthermore, it is shown that 2-D minimum noise realizations are rotated and scaled balanced realizations. Using this property, 2-D minimum noise realizations are proved to be free of overflow oscillations under zero input conditions, if their second-order modes are distinct.

Adaptive filters suitable for real-time spectral analysis

Abstract: Some new cascade structures for adaptive filters are presented. They are especially suitable for real-time applications. Since the new structures are intended to be realized using single chip DSP IC's or single chip custom VLSI circuits the requirements for memory and divisions are minimized. The new structures are based on state-variable biquads that in addition to having good SNR's and low sensitivities (for fixed-point implementations) can also have their resonant frequencies and Q -factors independently tuned. The special cass of using the adaptive filters for tracking sinusoids corrupted by noise and for formant based speech compression are described in detail.

A common structure for recursive discrete transforms

Abstract: This paper presents a common framework for the recursive implementation of arbitrary discrete transformations. The transform coefficients to be applied are periodically time-varying and can be derived from the discrete basis functions of the transforms. The method is based on Hostetter's dead-beat observer approach to signal processing [1], [2], but instead of the ongoing calculation of the transform coefficients, explicit expressions are derived. The proposed structure can be efficiently used even for FIR and IIR filtering operations.

Synthesis of 2-D state-space fixed-point digital-filter structures with minimum roundoff noise

Abstract: Based on a roundoff-noise analysis, a general synthesis procedure is developed which leads to an optimal local state-space 2-D digital-filter realization that minimizes the output-noise power due to roundoff subject to a scaling condition on the state variables. The outputnoise power and the signal scaling condition are closely related to two positive-definite matrices W and K . These matrices provide two sets of invariants, called the 2-D second-order modes of the filter, which play a crucial role in the minimization of the output-noise power. With the availability of matrices W and K , the 2-D similarity transformation that yields an optimal state-space realization can be obtained by solving separately two 1-D optimization problems so that the well-developed techniques for minimizing roundoff noise in 1-D state-space digital filters can also be used for minimizing roundoff noise in 2-D state-space digital filters.

Synthesis and analysis of state-space active filters using intermediate transfer functions

Abstract: This paper is concerned with the realization of a given arbitrary filter transfer function as a network of resistively interconnected integrators. These state-space realizations are synthesized using a new technique called intermediate function (IF) synthesis. The technique is based on the selection of a set of functions to serve as either the transfer functions from the filter input to the integrator outputs or the transfer functions from the integrator inputs to the filter output. Relationships between the filter sensitivity and dynamic range and the intermediate functions are derived. A number of results are also given to aid in the selection of a set of IF's that yields structures with optimum performance.

Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

Abstract: A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of M FIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included.

Charge redistribution and noise margins in domino CMOS logic

Abstract: Domino CMOS gates suffer from an inherent noise margin problem as a result of charge redistribution between parasitic capacitances at internal nodes of the circuit under specific input conditions. This charge redistribution effect can destroy the noise margin and cause glitches at the output of a domino gate. This paper deals with circuit and layout techniques which can help in alleviating the problem. A simple analytical noise margin model for domino gates is discussed. The model is useful to monitor the noise margins of a domino gate while dimensioning the devices in the gate to obtain a specified gate delay. A new technique which allows the design of domino gates with a very large fan-in (typically 20 or more inputs), while maintaining good noise margins and acceptable gate delays, is presented. This technique is useful in, for example, decoder circuits.

Theory and design of uniform DFT, parallel, quadrature mirror filter banks

Abstract: In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signal x(n) , are also derived using this concept. In general, the reconstructed. signal \hat{x}(n) suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, and \hat{x}(n) is equal to a delayed version of x(n)) of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework.

A unified study on the roundoff noise in 2-D state space digital filters

Abstract: This paper studies the roundoff noise and the scaling in 2-D state space digital filters. The noise matrix and the covariance matrix in the 2-D case are derived. They are expressed with double infinite sums or double integral. A formulation is presented to synthesize minimum roundoff noise 2-D state space digital filters. A practical synthesis procedure is also provided. A numerical example is given to show the analysis method and synthesis method presented here.

Extensions of a result on the synthesis of signals in the presence of inconsistent constraints

Abstract: Image restoration in the presence of compatible convex constraints can be carried out by the method of convex projections [1]-[3]. In a recent interesting paper [4], Goldburg and Marks have used a modified version of the above technique to solve an optimization problem involving the synthesis of a signal subject to two inconsistent constraints. We complete this result and also show that their restriction to a real Hilbert space setting is unnecessary. A unique generalization of the above optimization problem to the case of more than two constraints does not seem possible. Nevertheless, considerations of symmetry have led us to a formulation which identifies "minimizers" as "nodes" on closed "greedy" paths and an important and potentially useful property of such paths is proven in Theorem 4.