Showing papers on "Transfer function published in 1978"

Optimum synthesis of non-minimum phase feedback systems with plant uncertainty†

Abstract: Linear time-invariant feedback systems in which the constrained plant transfer function has right half-plane zeros, are perforce non-minimum-phase, and their attainable benefits of feedback are inherently restricted. This paper presents criteria for determining whether a given set of performance specifications are achievable and, if so, a synthesis procedure is included for deriving the optimum design, defined as that with an effectively minimum loop transmission bandwidth. The properties of the optimum design are derived and its uniqueness proven, for both the minimum and non-minimum-phase feedback systems.

Block implementation of recursive digital filters--New structures and properties

Abstract: Several new structures for the block implementation of HilR digital filters are proposed. The relation between the pole locations of the block structure to that of the original scalar transfer function is derived. A method to obtain the scalar transfer function from a given block structure is described.

On first-order equations for multidimensional filters

Abstract: A construction is given to obtain first-order equation representations of a multidimensional filter, whose dimension is of the order of the degree of the transfer function.

Some difficulties with the double bilinear transformation in 2-D recursive filter design

Abstract: It is shown that the double bilinear transformation approach for designing a 2-D IIR digital transfer function from a predetermined 2-D analog transfer function, may in certain cases lead to unstable solutions.

Stage-expanded stereophonic sound reproduction

Abstract: A stereophonic reproduction system comprises a localization network receptive of sterophonic signals to localize of sonic images at desired locations. A crosstalk canceler, connected in tandem with the localization network, cancels acoustic crosstalk interference. The localization network comprises in each channel a first adder providing algebraic summation of the input signal of the own channel and a negative feedback signal supplied from its output through a first subtractor and through a first transfer circuit having a transfer function representing the ratio of hypothetical crosstalk path transfer function to hypothetical direct path transfer function. The subtractor also responds to the signal of the other channel to algebraically combine the received signal in phase through the first transfer circuit with the input signal of the own channel. The crosstalk canceler comprises in each channel a second adder providing algebraic summation of the signal from the first adder and the signal of the same channel through a second subtractor and a second transfer circuit having a transfer function representing the ratio of actual crosstalk path transfer function to actual direct path transfer function. The second subtractor also responds to the signal from the second adder of the other channel to combine the received signal with the signal from the first adder in opposite phase through the second transfer circuit. Attenuators permit manual adjustment of signals supplied to the first and second subtractors of each channel.

Control method utilizing a model control scheme

Abstract: A control method is described in which, a plant, a reference model and a corrector are serially connected in the loop. The plant output is fed back and compared against a reference signal to develop an error signal. The reference mode operates upon the error signal with a predetermined transfer function to develop signals proportional to the error signal and various successive order derivatives of the error signal. The model output signals are applied to a corrector circuit which multiplies the respective model output signals by appropriate coefficients, and sums the resultant product signals to produce control signals for the plant. Provisions are also disclosed for varying the coefficients to provide self-adaptive control. Provisions for accommodating process delays are also provided.

Signal processing circuit for binaural signals

Abstract: A binaural signal processing circuit comprising a first system for imparting an input signal with a transfer characteristic equal to the transfer characteristic hL(t; θ, r) from a sound source to the left ear of a listener, where θ represents an angle between the front direction of the listener and the sound source, and r represents a distance between the sound source and the listener, a second system for imparting the input signal with a transfer characteristic equal to the transfer characteristic hR(t; θ, r) from the sound source to the right ear of the listener, a system for variably controlling the transfer functions of the first and second transfer function imparting systems, and a further system for deriving binaural signals from the first and second transfer function imparting systems.

Adaptive interference reduction system for crosstalk cancellation in a dual polarization system

Abstract: An adaptive interference reduction system for removing cross talk from a dual polarization system comprising a first adjustable filter for varying the phase and the weight of a first input signal, a second adjustable filter for varying the phase and the weight of a second input signal, a first adder for adding this first input signal and the weighted and phase adjusted output from the second adjustable filter, a second adder for adding the second input signal and the weighted and phase adjusted output from the first adjustable filter, a first noise-to-signal measuring device for generating a signal proportional to the noise-to-signal ratio in the output signal from the first adder, a second noise-to-signal measuring device for generating a signal proportional to the noise-to-signal ratio in the output signal from the second adder, and a dither-type control logic for dithering in-phase and quadrature square-waves in accordance with the signals generated by the first and second noise-to-signal measuring devices to control the first and second adjustable filters. This system is further characterized in that the first and second noise-to-signal measuring devices comprise a slow response control circuit for maintaining the average value of the input signal from the adder at a reference value, and means for filtering this averaged value and detecting the power fluctuations remaining in the signal and generating a signal proportional to these fluctuations. Additionally, the first and second adjustable filters may be structured to have transfer functions across a predetermined bandwidth of W 0 [1+W 1 ω+W 2 ω 2 ] or W 0 [1+W 1 ω+W 2 ω 2 +W 3 ω 3 ], where W 0 , W 1 , W 2 and W 3 are signal weights and ω represents the frequency variation of the input signal from its carrier.

On transfer function representations for homogeneous nonlinear systems

Abstract: For stationary, homogeneous, nonlinear systems described via the Volterra functional representation, the Laplace transform of the system kernel is commonly used as a "transfer function." Corresponding to the symmetric and triangular forms of the kernel, special forms are obtained for the transfer function. We propose a new form for both the time-domain and transform-domain representation of homogeneous systerns. Properties of these so-called regular forms in relation to the other two forms and in regard to input/output computation, stability, and bilinear realization theory are discussed.

The absolute stability of high-order discrete-time systems utilizing the saturation nonlinearity

Abstract: Previously, we investigated the stability of a class of discrete-time filters involving a restricted class of linear systems, the all-pole systems, and a single, specific, memoryless nonlinearity-the saturation nonlinearity. A rather effective criterion was derived for determining if a given system is free of all periodic oscillations except the trivial null solution. The derivation relied on the observation that certain rather exclusive properties, called passivity properties, are associated with the saturation nonlinearity. Here, we generalize the results in two directions. First, the linear part of the system is allowed to be quite general, i.e., both poles and zeros may occur in the transfer function. Thus in the context of digital filters, the restriction to the direct-form realization is lifted. Secondly, the criterion obtained here guarantees the absolute stability of the system and not just the absence of nontrivial periodic oscillations. Thus the possibility of aperiodic or "chaotic" behavior is eliminated. The broadened formulation enhances the utility of the criterion, making it applicable to the large class of recursive digital processing systems, including digital filters, which use the saturation arithmetic to cope with overflow in the course of forming the sum of the results of many multiplicative operations. Also, the methods developed indicate an approach for the stability investigation of large digital transmission networks containing nonlinearities. The technique used for deriving the new result is entirely different. The new element is the demonstration that the hypothesis which is in the form of a condition in the frequency domain implies the existence of a Lyapunov function.

Order reduction by ℓ 1 - and ℓ ∞ -norm minimization

Abstract: New procedures for order reduction, based on interpreting the system impulse response (or transfer function) as an input-output map, are presented. It is shown that some existing procedures for system simplification lead to unstable models.

Digital Control Law Synthesis in the w' Domain

Abstract: Utility of w' transform domain analysis/synthesis procedures for linear, constant, single-rate sampled-data systems is explored. Basic properties of the wf domain are reviewed and compared with corresponding Z-,H>-, and s-domain properties. The main contribution of the paper is recognition that sampling and data-hold operations are modeled exactly in the w' domain, regardless of the sampling rate employed, and that the w' variable is analogous to the s variable in the sense that all familiar frequency domain design concepts, procedures, and interpretations can be carried over directly. Moreover, the imaginary part of w' approximates angular frequency to for Ico 1 < ir/lT, which further facilitates interpretation. Two example applications illustrate the procedure and make clear (by means of transfer functions and Bode plots) the nonminimum phase effects of sampling and data-hold operations and of sampling rate. It is demonstrated that acceptable closed-loop performance can be achieved at sampling rates that are an order of magnitude less than those employed when an emulation design approach is used.

Design of selective linear-phase filters with equiripple amplitude characteristics

Abstract: A simple numerical technique is described for the construction of a nonminimum phase transfer function with an optimum equiripple passband amplitude response and linear-phase characteristics. The linearphase behavior may be maintained over part of or over the entire passband by varying the number of transmission zeros at infinity. Increasing the number increases the selectivity of the filter at the expense of a deterioration in the phase performance towards the edge of the passband. Synthesis is performed using even- and odd-mode decomposition, and tables of element values are provided with graphical design information to enable the design engineer to choose the correct prototype to meet a given specification.

Simultaneous magnitude and phase equalization using digital filters

Abstract: This paper presents a general method for designing digital filters in the frequency domain. The method is based on a Laurent expansion of the filter transfer function, H (z) , about the orgin. A special case of the method, developed in this paper, allows the coefficients of the polynomials containing the poles and zeros of H (z) to be determined by solving triangular linear equations in the Fourier coefficients of the prescribed magnitude and phase characteristics. Either finite-duration impulse-response (FIR) or infinite-duration impulse-response (IIR) filters can be designed by this method.

Epoch extraction from linear prediction residual

Abstract: An interpretation of linear prediction (LP) residual is presented by considering the effect of following factors: shape of glottal pulse, phase angles of formants at the instant of excitation, inaccurate estimation of formants and bandwidths, zeroes in vocal tract system transfer function. Effect of improper phase cancellation on the accuracy of estimated epoch position is also discussed. A method for unambiguous identification of epochs from LP residual is presented.

Frequency selectivity of the peripheral auditory analyzer studied using broad band noise.

Abstract: The sharpness of the frequency tuning of single auditory nerve fibers was studied in the rat on the basis of responses to broad band noise. The cross-spectra between the sound stimulus and the sound-to-stimulus locked discharge rate were used as estimates of the transfer functions of the peripheral auditory analyzer. The sharpness of the tuning obtained in that way was measured as Q3dB and Q10dB. It was found that these Q-values decreased with increasing stimulus intensity but that the decrease was different when it was based on measurements at 3 dB points of the obtained transfer functions compared with measuring it at 10 dB points. The change in width was less for fibers with low CF. In all the fibers studied the frequency of maximal response (CF) decreased with increasing sound intensity. The implication of these findings for pitch perception and for noise induced hearing loss is discussed.

Transfer functions for the seismic research observatory seismograph system

Abstract: Transfer functions are given for all basic elements of the Seismic Research Observatory (SRO) seismograph system. These include the seismometer, response shaping filters, and anti-alias filters. With these transfer functions the amplitude and phase responses can be calculated at any frequency by the evaluation of a ratio of polynomials in s = iω . Amplitude and phase response plots and impulse responses are given for the most important overall transfer functions. In addition, long- and short-period group delays have been calculated by numerical differentation of phase responses. In the long-period case a simple polynomial approximation to the group delay is given as an aid in interpretation of data. The transfer functions are exact and follow from the integral design of the system.

Robust Stability of Linear Dynamic Systems with Application to Singular Perturbation Theory

Abstract: In this paper we will give a simple approach to determining conditions for stability of linear feedback systems subject to additive and multiplicative perturbations in the operators describing these systems. The approach is based on techniques used in functional analysis, and provides an alternative development and generalization of some conditions for the time - invariant case that have appeared in the literature very recently. As an example of the application of the conditions, we consider the determination of finite regions of stability for singularly perturbed systems.

Linearization technique for closed-loop acousto-optic modulators

Abstract: Linearization of a closed-loop acousto-optic modulation system is maintained over a uniform closed-loop bandwidth that is independent of the output light intensity level through the use of a compensating square-root function generator which employs the third quadrant characteristic of a MOSFET. The MOSFET may be connected as the feedback impedance of an operational amplifier which provides the square-root gain control function for complementing the non-linearity of the acousto-optic modulator. By utilizing the third quadrant characteristics of the source-to-drain voltage relative to the drain current of the MOSFET, the square-root function generator has a transfer function which insures that a linear relationship between modulator output light intensity and input signal current can be obtained irrespective of light intensity. In accordance with a preferred embodiment of the present invention, the operational amplifier of the square-root function generator may be supplied with an offset voltage in order to insure that the desired square-root transfer function can be attained regardless of differences in the manufactured characteristics of the field effect transistors that may be used. Temperature compensation circuitry may also be adopted as part of the square-root gain control component of the system to counteract the temperature sensitivity of the MOSFET's square-root current-voltage characteristic.

Vehicle Response to Stochastic Roadways

Abstract: SUMMARY Dynamic response calculations for vehicles traversing irregular surfaces are usually accomplished using frequency domain methods involving spectral densities and transfer functions. Here an alternative procedure is developed which allows direct computation of mean square values and correlations of system variables for both transient and steady-state conditions. The method is based upon the differential equation for the covariance matrix which is directly related to the state equations for the vehicle. Multiple white noise inputs can be incorporated as well as inputs at two wheels which follow the same track at a distance from one another..The method is suitable for computer implementation without the complex algebra associated with finding all necessary transfer functions and the necessity of evaluating integrals in order to find mean square values using the conventional approach. As an illustration, a simple vehicle model is worked out completely and the variation of pitch and heave motion as a f...

An Experimental Application of Time Delay Compensation Techniques to Distillation Column Control

Abstract: Two time delay compensation techniques, the Smith predictor and the “analytical predictor”, are used to control top composition of a pilot scale distillation column. In each control scheme the predictive model consists of a first order plus time delay transfer function developed empirically from open-loop data. Experimental and simulation studies are used to evaluate the predictive control schemes and to compare their performance with conventional PI control.

A new realization method for 2-D digital transfer functions

Abstract: This paper presents a general method for realizing an arbitrary 2-D digital transfer function. The realizations are obtained in terms of two types of delay blocks, adders and multipliers. The techniques presented here can be used to obtain infinitely many realizations of the same transfer function.

A state-space realization for transfer functions

Abstract: This paper presents a new approach to the realization of rational transfer functions via state-variable methods. The resulting structures use an RC ladder network, n voltage followers, and two summers with appropriate scalings, where n is the degree of the characteristic polynomial of the given transfer function. The nonsingular transformation matrix Q that relates two state-space realizations plays an important role in our approach.

Transfer-function modelling of arteries.

Abstract: The paper describes a method for processing input/output blood velocity waveforms for femoral arteries obtained from ultrasonic Doppler flowmeters. Normal, diseased and early cases of disease are discussed, and it is shown that a pictorial display of the roots of a quadratic equation provide a simple quantitative assessment of progress and treatment of disease

Introduction to filter theory

Abstract: dix A. Even if you don’t choose to memorize them this system aids in reference and retreival of important formulas. The book was compiled from notes developed during eight years of teaching a graduate course on the subject and was used as a text. Thus it has been student tested. Appendix F contains a number of problems, grouped to be used on a chapter by chapter basis The problems are designed to illustrate practical applications of the text material. The parts of this book of most interest and value to the EMC engineer will be the chapters on Thermal Noise, Antennas, Propagation and Transmission Lines, and Reflection and Refraction. This is not to downpade the chapters on Statistics and Its Applications, Signal Processing and Detection, and Some System Characteristics which also contain much potentially useful materials. Additional plus values for the book include a list of 40 references, a table of symbols used throughout the book, and a subject index. Some readers may find the condensed type and close line spacing hard to read. It was apparently set up by typewriter using an elite type face with single line spacing. When reduced down to a 6 by 9 5 inch size page it is too crowded for easy reading. In spite of this shortcoming your reviewer recommends this book as a worthwhile reference in this field of interest.

Time Constants and Learning Curves of LMS Adaptive Filters.

Abstract: : This paper treats the convergence of adaptive LMS filters and, in particular, the adaptive line enhancer (ALE). The learning curves of such a filter are a sum of exponentially decaying modes with time constants given by the eigenvalues of the input correlation matrix and the relative initial magnitudes given by the projections of the filter on the eigenvectors. It is shown that, for large filter lengths, a simple correspondence may be set up between the discrete and continuous cases. Indexed by frequency, the eigenvalues of the correlation matrix correspond to the magnitude of the power spectrum, and the projections onto the eigenvectors to the filter transfer function. A detailed analysis is carried out for single pole spectra and evaluated through a computer simulation. In general, the techniques developed provide a physical context, i.e., the signal spectrum, in which to evaluate convergence. Thus, it is possible, with varying degrees of accuracy depending on knowledge of the input spectrum, to predict the convergence behavior of the system in general. (Author)

Availability of a Redundant System

Abstract: The Laplace transform of the availability of a multicomponent system with spares, is obtained by the regeneration point technique.