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NASA NTRS1991

On optimal infinite impulse response edge detection filters

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Sarkar, Sudeep↗

NASA NTRS2002

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

Rabinowitz, Matthew↗

NASA NTRS1992

An IIR median hybrid filter

A new class of nonlinear filters, the so-called class of multidirectional infinite impulse response median hybrid filters, is presented and analyzed. The input signal is processed twice using a linear shift-invariant infinite impulse response filtering module: once with normal causality and a second time with inverted causality. The final output of the MIMH filter is the median of the two-directional outputs and the original input signal. Thus, the MIMH filter is a concatenation of linear filtering and nonlinear filtering (a median filtering module). Because of this unique scheme, the MIMH filter possesses many desirable properties which are both proven and analyzed (including impulse removal, step preservation, and noise suppression). A comparison to other existing median type filters is also provided.

Bauer, Peter H.↗

NASA NTRS2002

Adaptive Identification and Control of Flow-Induced Cavity Oscillations

Progress towards an adaptive self-tuning regulator (STR) for the cavity tone problem is discussed in this paper. Adaptive system identification algorithms were applied to an experimental cavity-flow tested as a prerequisite to control. In addition, a simple digital controller and a piezoelectric bimorph actuator were used to demonstrate multiple tone suppression. The control tests at Mach numbers of 0.275, 0.40, and 0.60 indicated approx. = 7dB tone reductions at multiple frequencies. Several different adaptive system identification algorithms were applied at a single freestream Mach number of 0.275. Adaptive finite-impulse response (FIR) filters of orders up to N = 100 were found to be unsuitable for modeling the cavity flow dynamics. Adaptive infinite-impulse response (IIR) filters of comparable order better captured the system dynamics. Two recursive algorithms, the least-mean square (LMS) and the recursive-least square (RLS), were utilized to update the adaptive filter coefficients. Given the sample-time requirements imposed by the cavity flow dynamics, the computational simplicity of the least mean squares (LMS) algorithm is advantageous for real-time control.

Kegerise, M. A.↗

NASA NTRS1994

Low-complexity wavelet filter design for image compression

Image compression algorithms based on the wavelet transform are an increasingly attractive and flexible alternative to other algorithms based on block orthogonal transforms. While the design of orthogonal wavelet filters has been studied in significant depth, the design of nonorthogonal wavelet filters, such as linear-phase (LP) filters, has not yet reached that point. Of particular interest are wavelet transforms with low complexity at the encoder. In this article, we present known and new parameterizations of the two families of LP perfect reconstruction (PR) filters. The first family is that of all PR LP filters with finite impulse response (FIR), with equal complexity at the encoder and decoder. The second family is one of LP PR filters, which are FIR at the encoder and infinite impulse response (IIR) at the decoder, i.e., with controllable encoder complexity. These parameterizations are used to optimize the subband/wavelet transform coding gain, as defined for nonorthogonal wavelet transforms. Optimal LP wavelet filters are given for low levels of encoder complexity, as well as their corresponding integer approximations, to allow for applications limited to using integer arithmetic. These optimal LP filters yield larger coding gains than orthogonal filters with an equivalent complexity. The parameterizations described in this article can be used for the optimization of any other appropriate objective function.

Majani, E.↗

NASA NTRS1980

Distributed parameter system coupled ARMA expansion identification and adaptive parallel IIR filtering - A unified problem statement

A novel interconnection of distributed parameter system (DPS) identification and adaptive filtering is presented, which culminates in a common statement of coupled autoregressive, moving-average expansion or parallel infinite impulse response configuration adaptive parameterization. The common restricted complexity filter objectives are seen as similar to the reduced-order requirements of the DPS expansion description. The interconnection presents the possibility of an exchange of problem formulations and solution approaches not yet easily addressed in the common finite dimensional lumped-parameter system context. It is concluded that the shared problems raised are nevertheless many and difficult.

Johnson, C. R., Jr.↗

NASA NTRS1989

The effects of clutter-rejection filtering on estimating weather spectrum parameters

The effects of clutter-rejection filtering on estimating the weather parameters from pulse Doppler radar measurement data are investigated. The pulse pair method of estimating the spectrum mean and spectrum width of the weather is emphasized. The loss of sensitivity, a measure of the signal power lost due to filtering, is also considered. A flexible software tool developed to investigate these effects is described. It allows for simulated weather radar data, in which the user specifies an underlying truncated Gaussian spectrum, as well as for externally generated data which may be real or simulated. The filter may be implemented in either the time or the frequency domain. The software tool is validated by comparing unfiltered spectrum mean and width estimates to their true values, and by reproducing previously published results. The effects on the weather parameter estimates using simulated weather-only data are evaluated for five filters: an ideal filter, two infinite impulse response filters, and two finite impulse response filters. Results considering external data, consisting of weather and clutter data, are evaluated on a range cell by range cell basis. Finally, it is shown theoretically and by computer simulation that a linear phase response is not required for a clutter rejection filter preceeding pulse-pair parameter estimation.

Davis, W. T.↗

NASA NTRS1990

A class of systolizable IIR digital filters and its design for proper scaling and minimum output roundoff noise

A class of infinite impulse response (IIR) digital filters with a systolizable structure is proposed and its synthesis is investigated. The systolizable structure consists of pipelineable regular modules with local connections and is suitable for VLSI implementation. It is capable of achieving high performance as well as high throughput. This class of filter structure provides certain degrees of freedom that can be used to obtain some desirable properties for the filter. Techniques of evaluating the internal signal powers and the output roundoff noise of the proposed filter structure are developed. Based upon these techniques, a well-scaled IIR digital filter with minimum output roundoff noise is designed using a local optimization approach. The internal signals of all the modes of this filter are scaled to unity in the l2-norm sense. Compared to the Rao-Kailath (1984) orthogonal digital filter and the Gray-Markel (1973) normalized-lattice digital filter, this filter has better scaling properties and lower output roundoff noise.

Lei, Shaw-Min↗

NASA NTRS1993

Symbol signal-to-noise ratio loss in square-wave subcarrier downconversion

This article presents the simulated results of the signal-to-noise ratio (SNR) loss in the process of a square-wave subcarrier down conversion. In a previous article, the SNR degradation was evaluated at the output of the down converter based on the signal and noise power change. Unlike in the previous article, the SNR loss is defined here as the difference between the actual and theoretical symbol SNR's for the same symbol-error rate at the output of the symbol matched filter. The results show that an average SNR loss of 0.3 dB can be achieved with tenth-order infinite impulse response (IIR) filters. This loss is a 0.2-dB increase over the SNR degradation in the previous analysis where neither the signal distortion nor the symbol detector was considered.

Feria, Y.↗

NASA NTRS1992

Spatially-varying IIR filter banks for image coding

This paper reports on the application of spatially variant infinite impulse response (IIR) filter banks to subband image coding. The new filter bank is based on computationally efficient recursive polyphase decompositions that dynamically change in response to the input signal. In the absence of quantization, reconstruction can be made exact. However, by proper choice of an adaptation scheme, we show that subband image coding based on time varying filter banks can yield improvement over the use of conventional filter banks.

Chung, Wilson C.↗

NASA NTRS1992

Recursive time-varying filter banks for subband image coding

Filter banks and wavelet decompositions that employ recursive filters have been considered previously and are recognized for their efficiency in partitioning the frequency spectrum. This paper presents an analysis of a new infinite impulse response (IIR) filter bank in which these computationally efficient filters may be changed adaptively in response to the input. The filter bank is presented and discussed in the context of finite-support signals with the intended application in subband image coding. In the absence of quantization errors, exact reconstruction can be achieved and by the proper choice of an adaptation scheme, it is shown that IIR time-varying filter banks can yield improvement over conventional ones.

Smith, Mark J. T.↗

NASA NTRS1993

Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction

The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.

Parker, B. Eugene, Jr.↗

NASA NTRS1968

An extension to the circle criterion.

Circle criterion for stability of nonlinear time varying systems, considering integrator and infinite sequence of impulses in impulse response

Desoer, C. A.↗

NASA NTRS1981

Modeling and control of flexible space structures

The effects of actuator and sensor locations on transfer function zeros are investigated, using uniform bars and beams as generic models of flexible space structures. It is shown how finite element codes may be used directly to calculate transfer function zeros. The impulse response predicted by finite-dimensional models is compared with the exact impulse response predicted by the infinite dimensional models. It is shown that some flexible structures behave as if there were a direct transmission between actuator and sensor (equal numbers of zeros and poles in the transfer function). Finally, natural damping models for a vibrating beam are investigated since natural damping has a strong influence on the appropriate active control logic for a flexible structure.

Wie, B.↗

NASA NTRS1996

Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics

Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.

Watson, Willie R.↗

NASA NTRS1973

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Callier, F. M.↗

NASA NTRS1998

A Solution to the Fundamental Linear Fractional Order Differential Equation

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Hartley, Tom T.↗

NASA NTRS1991

Interface behavior of a multi-layer fluid configuration subject to acceleration in a microgravity environment, supplement 1

With the increasing opportunities for research in a microgravity environment, there arises a need for understanding fluid mechanics under such conditions. In particular, a number of material processing configurations involve fluid-fluid interfaces which may experience instabilities in the presence of external forcing. In a microgravity environment, these accelerations may be periodic or impulse-type in nature. This research investigates the behavior of a multi-layer idealized fluid configuration which is infinite in extent. The analysis is linear, and each fluid region is considered inviscid, incompressible, and immiscible. An initial parametric study of confiquration stability in the presence of a constant acceleration field is performed. The zero mean gravity limit case serves as the base state for the subsequent time-dependent forcing cases. A stability analysis of the multi-layer fluid system in the presence of periodic forcing is investigated. Floquet theory is utilized. A parameter study is performed, and regions of stability are identified. For the impulse-type forcing case, asymptotic stability is established for the configuration. Using numerical integration, the time response of the interfaces is determined.

Lyell, M. J.↗