Showing papers in "Circuits Systems and Signal Processing in 1999"

Spectral mimicry: A method of synthesizing matching time series with different Fourier spectra

Abstract: Given a stationary time seriesX and another stationary time seriesY (with a different power spectral density), we describe an algorithm for constructing a stationary time series Z that contains exactly the same values asX permuted in an order such that the power spectral density ofZ closely resembles that ofY. We call this methodspectral mimicry. We prove (under certain restrictions) that, if the univariate cumulative distribution function (CDF) ofX is identical to the CDF ofY, then the power spectral density ofZ equals the power spectral density ofY. We also show, for a class of examples, that when the CDFs ofX andY differ modestly, the power spectral density ofZ closely approximates the power spectral density ofY. The algorithm, developed to design an experiment in microbial population dynamics, has a variety of other applications.

On Kalman's controllability and observability criteria for singular systems

Abstract: The controllability and observability properties of a singular system are extensively studied. The definitions of controllability,R-controllability, and impulse controllability are introduced via characteristics of the original state vector. Analogous definitions are presented for the case of observability. The criteria established for controllability and observability are simple rank criteria related to the Markov parameters from the inputs to the states and from the initial conditions to the outputs, respectively. The present results can be considered as the direct extension of Kalman's controllability and observability criteria to the case of singular systems. Finally, the controllability and observability subspaces are derived from the image and the kernel of the controllability and the observability matrices, respectively.

Constructing analytical energy functions for lossless network-reduction power system models: Framework and new developments

Abstract: The task of constructing an energy function is essential for direct stability analysis of electric power systems. This paper presents a general procedure for constructing analytical energy functions for detailed lossless network-reduction power system stability models. This paper primarily (i) develops canonical representations for lossless networkreduction power system models and shows that such canonical representations cover existing stability models, (ii) derives theoretical results regarding the existence of analytical energy functions for the canonical representations, and (iii) presents a systematic procedure to construct corresponding energy functions.

On the direction estimation Cramér-Rao bounds in the presence of uncorrelated unknown noise

Abstract: The deterministic and stochastic direction estimation Cramer-Rao bounds (CRBs) are studied in the presence of one signal and spatially uncorrelated sensor noise with unknown nonequal variances in array sensors. The explicit CRB expressions are obtained, and their relationship is studied showing some typical properties inherent in the nonidentical noise case.

Two-dimensional discrete-continuous model conversion

Abstract: This paper presents a geometric-series method for finding two-dimensional (2D) discrete-time (continuous-time) state-space models from 2D continuous-time (discretetime) systems. This method allows the use of well-developed theorems and algorithms in the 2D discrete-time (continuous-time) domain to indirectly carry out analysis and design of hybrid 2D composite systems.

Uncorrelated component analysis for blind source separation

Abstract: The uncorrelated component analysis (UCA) of a stationary random vector process consists of searching for a linear transformation that minimizes the temporal correlation between its components. Through a general analysis we show that under practically reasonable and mild conditions UCA is a solution for blind source separation. The theorems proposed in this paper for UCA provide useful insights for developing practical algorithms. UCA explores the temporal information of the signals, whereas independent component analysis (ICA) explores the spatial information; thus UCA can be applied for source separation in some cases where ICA cannot. For blind source separation, combining ICA and UCA may give improved performance because more information can be utilized. The concept of single UCA (SUCA) is also proposed, which leads to sequential source separation.

Spread-spectrum signals and the chaotic logistic map

Abstract: Chaotic systems provide a simple means of generating deterministic signals that resemble white noise. It is this noise-like property that provides the potential for applying chaotic systems in communications. In this work, we report a detailed study of the logistic map for use as direct-sequence spread-spectrum (DS/SS) codes. The advantages of the chaotic DS/SS codes are the almost unlimited number of distinct sequences of arbitrary lengths, the ease of generating these sequences, and the increased privacy afforded by the noise-like appearance of these sequences. Some design criteria are provided from the correlation properties of these sequences, and bit-error rate (BER) results are generated by Monte Carlo simulations.

Envelope-constrained H2 FIR filter design

Abstract: In this paper, we consider an envelope-constrained (EC)H 2 optimal finite impulse response (FIR) filtering problem. Our aim is to design a filter such that theH 2 norm of the filtering error transfer function is minimized subject to the constraint that the filter output with a given input to the signal system is contained or bounded by a prescribed envelope. The filter design problem is formulated as a standard optimization problem with linear matrix inequality (LMI) constraints. Furthermore, by relaxing theH 2 norm constraint, we propose a robust ECFIR filter design algorithm based on the LMI approach.

Stabilization of Subba Rao-Liporace models

Abstract: The stability of time-varying autoregressive (TVAR) models is an important issue in many applications such as time-varying spectral estimation, EEG simulation and analysis, and time-varying linear prediction coding (TVLPC). For stationary AR models there are methods that guarantee stability, but the for nonadaptive time-varying approaches there are no such methods. On the other hand, in some situations, such as in EEG analysis, the models that temporarily exhibit roots with almost unit moduli are difficult to use. Thus we may need a tighter stability condition such as stability with margin 1??. In this paper we propose a method for the estimation of TVAR models that guarantees stability with margin 1??, that is, the moduli of the roots of the time-varying characteristic polynomial are less than or equal to some arbitrary positive number ? for every time instant. The model class is the Subba Rao-Liporace class, in which the time-varying coefficients are constrained to a subspace of the coefficient time evolutions. The method is based on sequential linearization of the associated nonlinear constraints and the subsequent use of a Gauss-Newton-type algorithm. The method is also applied to a simulated autoregressive process.

A numerical algorithm for the diffusion equation using 3D FEM and the Arnoldi method

Abstract: In this paper we introduce a new computational method for solving the diffusion equation. In particular, we construct a "generalized" state-space system and compute the impulse response of an equivalent truncated state-space system. In this effort, we use a 3D finite element method (FEM) to obtain the state-space system. We then use the Arnoldi iteration to approximate the state impulse response by projecting on the dominant controllable subspace. The idea exploited here is the approximation of the impulse response of the linear system. We study the homogeneous and heterogeneous cases and discuss the approximation error. Finally, we compare our computational results to our experimental setup.

Optimal design of nonuniform multirate filter banks

Abstract: The design of general nonuniform filter banks is studied. Contrary to uniform filter banks, in nonuniform filter banks, it may not be possible to achieve perfect reconstruction, but in some cases by using optimization techniques, we can design acceptable filter banks. Here, the initial finite impulse response (FIR) analysis filters are designed according to the characteristics of the input. By the design procedure, the FIR synthesis filters are found so that theH-norm of an error system is minimized over all synthesis filters that have a prespecified order. Then, the synthesis filters obtained in the previous step are fixed, and the analysis filters are found similarly. By iteration, theH-norm of the error system decreases until it converges to its final value. At each iteration, the coefficients of the analysis or synthesis filters are obtained by finding the least squares solution of a system of linear equations. If necessary, the frequency characteristics of the filters can be altered by adding penalty terms to the objective function.

Linear systems in a saturated mode and convergence as gain becomes large of asymptotically stable equilibrium points of neural nets

Abstract: We study solutions of the "linear system in a saturated mode" $$\begin{array}{*{20}c} {(M)} & {x' \in Tx + c - \partial I_{D^n } x.} \\ \end{array} $$ We show that a trajectory is in a constant face of the cubeD n on some interval (0,d]. We answer a question about comparing the two systems: (M) and $$\begin{array}{*{20}c} {(H)} & {\begin{array}{*{20}c} {Cu' = T\upsilon + c - R^{ - 1} u,} & {\upsilon = G(\lambda } \\ \end{array} u)} \\ \end{array} $$ . As ???, limits ofv corresponding to asymptotically stable equilibrium points of (H) are asymptotically stable equilibrium points of (M), and the converse is also true. We study the assumptions to see which are required and which may be weakened.

Minimax controller design using rate feedback

Abstract: A complete analytic characterization and solution construction (done either explicitly or by recursion) for the minimax control problem using optimal rate feedback is given for the case when the plant consists of a known fixed set of coupled oscillators of cardinality not exceeding three. When this is not the case, the problem appears to be analytically intractable, and suboptimal solutions based on numerical techniques are currently the only recourse.

A concurrent system for the computation of higher-order moments

Abstract: The cumulants defined in terms of moments are basic to the study of higher-order statistics (HOS) of a stationary stochastic process. This paper presents a concurrent systolic array system for the computation of higher-order moments. The system allows for the simultaneous computation of the second-, third-, and fourth-order moments. The architecture achieves good speedup through its excellent exploitation of parallelism, pipelining, and reusability of some intermediate results. The computational complexity and system performance issues related to the architecture are discussed. The concurrent system is designed with the CMOS VLSI technology and is capable of operating at 3.9 MHz.

Asymptotic behavior of block floating-point digital filters

Abstract: The asymptotic behavior of block floating-point and floating-point digital filters is analyzed. As a result, mantissa wordlength conditions are derived guaranteeing the absence of limit cycles in the regular dynamic range. Explicitly, the requirements are given for block floating-point state space filters with different quantization formats. Although these conditions are only sufficient, examples are given in which they are also necessary. In most cases the conditions are easily satisfied.

Linear phase FIR approximation of magnitude response

Abstract: In many signal processing situations, the desired (ideal) magnitude response of the filter is a rational function: $$\tilde H(\omega ) = |1/\omega |$$ (a digital integrator). The requirements of a linear phase response and guaranteed stable performance limit the design to a finite impulse response (FIR) structure. In many applications we require the FIR filter to yield a highly accurate magnitude response for a narrow band of frequencies with maximal flatness at an arbitrary frequency? 0 in the spectrum (0, ?). No techniques for meeting such requirements with respect to approximation of $$\tilde H(\omega )$$ are known in the literature. This paper suggests a design by which the linear phase magnitude response $$|\tilde H(\omega )|$$ can be approximated by an FIR configuration giving a maximally flat (in the Butterworth sense) response at an arbitrary frequency ?0, 0

A canonical form for discrete-time systems defined overZ+*

Abstract: It is shown that for each memberG of a large class of causal time invariant nonlinear input-output maps, with inputs and outputs defined on the nonnegative integers, there is a functionalA on the input set such that (Gs)(k) has the representationA(F k s) for allk and each inputs, in whichF k is a simple linear map that does not depend onG. More specifically, this holds--with anA that is unique in a certain important sense--for anyG that has approximately finite memory and meets a certain often-satisfied additional condition. Similar results are given for a corresponding continuous-time case in which inputs and outputs are defined on ?+. An example shows that the members of a large family of feedback systems have these "A-map" representations.

Finding all the DC solutions of a certain class of piecewise-linear circuits

Abstract: The problem of finding all the DC solutions of a certain class of piecewise-linear electronic circuits containing locally passive and locally active one-ports is considered in this paper. An effective method enabling us to locate the solutions is developed. The method constitutes the crucial point of an algorithm based on the idea of successive contraction, division, and elimination that is capable of determining all the solutions. Several numerical examples are given, and some comparison analyses are performed confirming the usefulness of the proposed approach.

Cycloid decompositions of finite Markov chains

Abstract: Finite homogeneous Markov chains ?, which admit invariant probability distributions, can be defined by the cycloids { $$\bar C_k $$ } (closed polygonal lines whose consecutive edges have various orientations that do not necessarily determine a common direction for $$\bar C_k $$ ) occurring in their graphs. These Markov chains are called cycloid chains, and the corresponding finite-dimensional distributions are linear expressions on the cycloids { $$\bar C_k $$ } with the real coefficients ?k. Then the collection {{ $$\bar C_k $$ }, {?k}}, called the cycloid decomposition of ?, gives a minimal description of the finite-dimensional distributions that, except for a choice of the maximal tree, uniquely determines the chain ?. Furthermore, the cycloid decompositions have an interpretation in terms of the transition probability functions expressing the same essence as the known Chapman-Kolmogorov equations.

A method for defining analog circuits for the minimization of discrete functionals: An image processing application

Abstract: The solutions of many physical-mathematical problems can be obtained by minimizing proper functionals. In the literature, some methods for the synthesis of analog circuits (mainly cellular neural networks) are presented that find the solution of some of these problems by implementing the discretized Euler-Lagrange equations associated with the pertinent functionals. In this paper, we propose a method for defining analog circuits that directly minimize (in a parallel way) a class of discretized functionals in the frequently occurring case where the solution depends on two spatial variables. The method is a generalization of the one presented in Parodi et al.,Internat. J. Circuit Theory Appl., 26, 477---498, 1998. The analog circuits consist of both a (nonlinear) resistive part and a set of linear capacitors, whose steady-state voltages represent the discrete solution to the problem. The method is based on the potential (co-content) functions associated with voltage-controlled resistive elements. es an example, we describe an application in the field of image processing: the restoration of color images corrupted by additive noise.

An adaptive Gauss-Newton algorithm for training multilayer nonlinear filters that have embedded memory

Abstract: We describe herein a new means of training dynamic multilayer nonlinear adaptive filters, orneural networks. We restrict our discussion to multilayer dynamic Volterra networks, which are structured so as to restrict their degrees of computational freedom, based on a priori knowledge about the dynamic operation to be emulated. The networks consist of linear dynamic filters together with nonlinear generalized single-layer subnets. We describe how a Newton-like optimization strategy can be applied to these dynamic architectures and detail a newmodified Gauss-Newton optimization technique. The new training algorithm converges faster and to a smaller value of cost than backpropagation-through-time for a wide range of adaptive filtering applications. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system. The superior performance of the algorithm over standard techniques is demonstrated.

The invertibility of operators and contraction mappings

Abstract: Necessary and sufficient conditions for the invertibility of a (not necessarily linear) operatorN between normed linear spaces are given. It is shown thatN is invertible precisely if a certain operator associated withN is a contraction.

A novel algorithm for computing autocorrelation of randomly sampled sequences

Abstract: Random sampling is one of the methods used to achieve sub-Nyquist sampling. This paper proposes a novel algorithm to evaluate the circular autocorrelation of a randomly sampled sequence, from which its power density spectrum can be obtained. With uniform sampling, the size of each lag (the step size) for computing an autocorrelation of a sequence is the same as the sampling period. When random sampling is adopted, the step size should be chosen such that the highest-frequency component of interest contained in a sequence can be accommodated. To find overlaps between a time sequence and its shifted version, an appropriate window is opened in one of the time sequences. To speed up the process, a marker is set to limit the range of searching for overlaps. The proposed method of estimating the power spectrum via autocorrelation is comparable in terms of accuracy and signal-to-noise ratio (SNR) to the conventional point rule. The techniques introduced can also apply to other operations for randomly sampled sequences.

Stabilization of third-order, single-stage Sigma-Delta modulators

Abstract: The issue of stability of higher-order, single-stage Sigma-Delta (ΣΔ) modulators is addressed using a method from nonlinear system theory. As a result, theoretical bounds for the quantizer input of the modulators are derived. A new method for stabilizing the ΣΔ modulators is then presented. It uses the quantizer input bound for possible instability detection. Upon detection of such a state, the highest-order integrator is cut off, effectively reducing the order of the modulator, and thus resulting in a stable system. The method is easily implemented and results in a very good signal-to-noise ratio (SNR) and fast return to normal operation compared to other stabilization methods.

Real-time FFT algorithm applied to on-line spectral analysis

Abstract: On-line running spectral analysis is of considerable interest in many electrophysiological signals, such as the EEG (electroencephalograph). This paper presents a new method of implementing the fast Fourier transform (FFT) algorithm. Our "real-time FFT algorithm" efficiently utilizes computer time to perform the FFT computation while data acquisition proceeds so that local butterfly modules are built using the data points that are already available. The real-time FFT algorithm is developed using the decimation-in-time split-radix FFT (DIT sr-FFT) butterfly structure. In order to demonstate the synchronization ability of the proposed algorithm, the authors develop a method of evaluating the number of arithmetic operations that it requires. Both the derivation and the experimental result show that the real-time FFT algorithm is superior to the conventional whole-block FFT algorithm in synchronizing with the data acquisition process. Given that the FFT sizeN=2 r , real-time implementation of the FFT algorithm requires only 2/r the computational time required by the whole-block FFT algorithm.

Stability analysis for rotating stall dynamics in axial flow compressors

Abstract: This paper analyzes the nonlinear phenomenon of rotating stall via the methods of projection [Elementary Stability and Bifurcation Theory, G. Iooss and D. D. Joseph, Springer-Verlag, 1980] and Lyapunov [J.-H. Fu,Math. Control Signal Systems, 7, 255---278, 1994]. A compressor model of Moore and Greitzer is adopted in which rotating stall dynamics are associated with Hopf bifurcations. Local stability for each pair of the critical modes is studied and characterized. It is shown that local stability of individual pairs of the critical modes determines collectively local stability of the compressor model. Explicit conditions are obtained for local stability of rotating stall which offer new insight into the design, and active control of axial flow compressors.

Permissively structured transfinite electrical networks

Abstract: Transfinite electrical networks of ranks larger than 1 have previously been defined by arbitrarily joining together various infinite extremities through transfinite nodes that are independent of the networks' resistance values. Thus, some or all of those transfinite nodes may remain ineffective in transmitting current "through infinity." In this paper, transfinite nodes are defined in terms of the paths that permit currents to "reach infinity." This is accomplished by defining a suitable metricd v on the node setN S v of eachv-sectionS v, av-section being a maximal subnetwork whose nodes are connected by two-ended paths of ranks no larger thanv. Upon taking the completion ofN S v under that metricd v, we identify those extremities (now calledv-terminals) that are accessible to current flows. These are used to define transfinite nodes that combine such extremities. The construction is recursive and is carried out through all the natural number ranks, and then through the first arrow rank � and the first limit-ordinal rank �. The recursion can be carried still further. All this provides a more natural development of transfinite networks and indeed simplifies the theory of electrical behavior for such networks.

Function emulation using MVQ neural networks

Abstract: In earlier studies a multiclass vector quantization (MVQ)-based neural network design was explored for pattern classification. We reconsider that design here in the context of function emulation. With proper adjustment, the MVQ design demonstrates excellent performance. Moreover, the design algorithms sense discontinuities in the data and replicate them in the network.

On singular nonlinear H ∞ control: A state-space approach

Abstract: A simple state-space approach for the four-block singular nonlinearH ? control problem is proposed in this paper. This approach combines a (J, J?)-lossless and a class of conjugate (J, J?)-expansive systems to yield a family of nonlinearH ? output feedback controllers. The singular nonlinearH ? control problem is thus transformed into a simple lossless network problem that is easy to deal with in a network-theory context.

Linear stabilizing controllers for electrically driven flexible-joint robots with uncertain parameters

Abstract: This study presents a linear output-based controller for stabilizing a rigid-link flexible-joint electrically driven (RLFJED) robot manipulator. The proposed controller ensures local exponential stability under some uncertainty conditions. It is assumed that the velocity signals from the link side are not measurable. The controller is analyzed by using tools for pole placement by an output-feedback in the framework of the linear system theory. Some useful structural properties of the systems under consideration have been studied. Applications of the results to the set-point regulation control problem are considered.