Showing papers on "Transfer function published in 2006"

Numerical Transform Inversion Using Gaussian Quadrature

Abstract: Numerical inversion of Laplace transforms is a powerful tool in computational probability. It greatly enhances the applicability of stochastic models in many fields. In this article we present a simple Laplace transform inversion algorithm that can compute the desired function values for a much larger class of Laplace transforms than the ones that can be inverted with the known methods in the literature. The algorithm can invert Laplace transforms of functions with discontinuities and singularities, even if we do not know the location of these discontinuities and singularities a priori. The algorithm only needs numerical values of the Laplace transform, is extremely fast, and the results are of almost machine precision. We also present a two-dimensional variant of the Laplace transform inversion algorithm. We illustrate the accuracy and robustness of the algorithms with various numerical examples.

A deterministic frequency-domain model for the indoor power line transfer function

Abstract: The characterization of the transfer function of the power line (PL) channel is a nontrivial task that requires a truly interdisciplinary approach. Until recently, a common attribute and limitation of existing models for the PL channel transfer function lay in the phenomenological or statistical approach usually followed. This approach allows one to describe the channel only partially, e.g., as dominated by multipath-like effects, and prevents one from unveiling special properties of it. Multiconductor transmission line (MTL) theory was recently found by the authors to be a useful and accurate tool in modeling the PL transfer function while, at the same time, taking into account the wiring and grounding practices mandated by several regulatory bodies for commercial and residential premises. Crossing several layers of abstraction and following a bottom-up approach, complex circuit-level models originating from MTL theory can be manipulated and represented in terms of cascaded two-port networks (2PNs), thus allowing one to compute a priori and in a deterministic fashion the transfer function of any PL link. In the present contribution, we present additional analysis and data that validate the accuracy of the MTL approach and further justify its use in the PL channel context. Moreover, we also describe in detail the methodology to follow for modeling both grounded and ungrounded PL links in a unified framework. A consequence of the validity of the proposed modeling is that it can facilitate the process of standardization of the PL transfer function, an important step toward the availability of a commonly agreed upon (set of) channel transfer functions.

Efficient Computation of Multivariable Transfer Function Dominant Poles Using Subspace Acceleration

Abstract: This paper describes a new algorithm to compute the dominant poles of a high-order multiple-input multiple-output (MIMO) transfer function. The algorithm, called the Subspace Accelerated MIMO Dominant Pole Algorithm (SAMDP), is able to compute the full set of dominant poles efficiently. SAMDP can be used to produce good modal equivalents automatically. The general algorithm is robust, applicable to both square and nonsquare transfer function matrices, and can easily be tuned to suit different practical system needs

Biased tomography schemes: an objective approach.

Abstract: We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done without the need for any ad hoc truncations of the Hilbert space. An illustration of this method is provided by a simple yet practically important tomography of an optical signal registered by realistic binary detectors.

Computation of Fractional Order Derivative and Integral via Power Series Expansion and Signal Modelling

Abstract: The three techniques of s-to-z transform, power series expansion (PSE) and signal modelling are combined to develop a new procedure for efficiently computing the fractional order derivatives and integrals of discrete-time signals. A mapping function between the s-plane and the z-plane is first chosen, and then a PSE of this mapping function raised to fractional order is performed to get the desired infinite impulse response of the ideal digital fractional operator. Finally, the desired impulse response is modelled as the impulse response of a linear invariant system whose rational transfer function is determined using deterministic signal modelling techniques. Three non-iterative techniques, namely Pade, Prony and Shanks’ methods have been considered in this paper. Using Al-Alaoui’s rule as s-to-z transform, computation examples show that both Prony and Shanks’ method can achieve more accurate fractional differentiation and integration than Pade method which is equivalent to continued fraction expansion technique.

A Method of Transformation from Symbolic Transfer Function to Active- RC Circuit by Admittance Matrix Expansion

Abstract: Active-RC circuits containing 2-terminal linear passive elements and ideal transistors or operational amplifiers are derived from symbolic voltage or current transfer functions by admittance matrix transformations without any prior assumption concerning circuit architecture or topology. Since the method is a reversal of symbolic circuit analysis by Gaussian elimination applied to a circuit nodal admittance matrix, it can generate all circuits using the specified elements that possess a given symbolic transfer function. The method is useful for synthesis of low-order circuits, such as those used for cascade implementation, for deriving alternative circuits with the same transfer function as an existing circuit or for realizing unusual transfer functions, as may arise, for example, where a transfer function is required that contains specific tuning parameters

Active control of boundary-layer instabilities

Abstract: Active control of spatially evolving three-dimensional instability waves in the boundary layer of a flat plate with zero pressure gradient has been investigated both numerically and experimentally. The boundary layer was artificially excited by various computer-generated perturbations in a low-turbulence wind tunnel so as to create a three-dimensional field of instability waves. Sensors were used to detect the oncoming disturbances and appropriate control signals sent to the downstream actuators to generate counteracting disturbances. The key element of this type of active control is the determination of the transfer function of the control system connecting the sensors with the actuators. Modelling by linear theory showed that the amplitudes of the disturbances downstream were significantly suppressed when the causal transfer function was applied. To simplify the control problem different strategies using approximations to the transfer function were used. It was shown that with a very simple transfer function almost the same result could be achieved as with the full causal transfer function. The modelling was validated experimentally, first by an offline control using different control modes, i.e. different transfer functions, and then by a real-time hardware implementation using one of the modes. Good agreement between the experimental measurements and numerical predictions indicated that a simple control strategy could be developed to inhibit the growth of the three-dimensional instability waves over extensive regions of the flow.

Algebraic Signal Processing Theory

Abstract: This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and phi generalizes the concept of the z-transform to bijective linear mappings from a vector space of, e.g., signal samples, into the module M. A signal model provides the structure for a particular linear signal processing application, such as infinite and finite discrete time, or infinite or finite discrete space, or the various forms of multidimensional linear signal processing. As soon as a signal model is chosen, basic ingredients follow, including the associated notions of filtering, spectrum, and Fourier transform. The shift operator is a key concept in the algebraic theory: it is the generator of the algebra of filters A. Once the shift is chosen, a well-defined methodology leads to the associated signal model. Different shifts correspond to infinite and finite time models with associated infinite and finite z-transforms, and to infinite and finite space models with associated infinite and finite C-transforms (that we introduce). In particular, we show that the 16 discrete cosine and sine transforms are Fourier transforms for the finite space models. Other definitions of the shift naturally lead to new signal models and to new transforms as associated Fourier transforms in one and higher dimensions, separable and non-separable. We explain in algebraic terms shift-invariance (the algebra of filters A is commutative), the role of boundary conditions and signal extensions, the connections between linear transforms and linear finite Gauss-Markov fields, and several other concepts and connections.

Minimax design of adjustable-bandwidth linear-phase FIR filters

Abstract: This paper considers the design of digital linear-phase finite-length impulse response (FIR) filters that have adjustable bandwidth(s) whereas the phase response is fixed. For this purpose, a structure is employed in which the overall transfer function is a weighted linear combination of fixed subfilters and where the weights are directly determined by the bandwidth(s). Minimax design techniques are introduced which generate globally optimal overall filters in the minimax (Chebyshev) sense over a whole set of filter specifications. The paper also introduces a new structure for bandstop and bandpass filters with individually adjustable upper and lower band edges, and with a substantially lower arithmetic complexity compared to structures that make use of two separate adjustable-bandwidth low-pass and high-pass filters in cascade or in parallel. Design examples are included in the paper.

Calibration of angle encoders using transfer functions

Abstract: Classical approaches to the calibration of angle encoders typically make use of circle division by means of an auxiliary artefact and apply linear equation systems constrained by circle closure which are solved for the errors of the encoder and those of the artefact simultaneously. Lately, emphasis has been placed on Fourier methods, as Fourier approaches involving transfer functions have proved to be a powerful tool applicable to various high-precision measurement tasks. We present an in-depth treatment of the use of the Fourier approach including transfer functions for the calibration of angle encoders. Different weighting schemes for combining the measurements will be presented by which the uncertainty of the calibration of angle encoders can be substantially reduced. The method utilizes angle difference measurements and it can therefore also be applied to the calibration of angle encoders using suitable arrangements of multiple reading heads. The approach is used for calibrating an angle encoder in an experimental set-up by means of a five-sided calibration polygon with angle differences between the optical faces that are not integer fractions of the full circle. The calibration results, including an evaluation of the measurement uncertainty, are presented for different weighting schemes and it is shown that appropriate weighting leads to a reduction in the uncertainty up to a factor of 4.

Automated tuning of large-scale multivariable model predictive controllers for spatially-distributed processes

Abstract: This paper presents an automated tuning method of a large-scale multivariable model predictive controller for multiple array paper machine cross-directional (CD) processes. Paper machine CD processes are large-scale spatially-distributed dynamical systems. Due to these systems' (almost) spatially invariant nature, the closed-loop transfer functions are approximated by transfer matrices with rectangular circulant matrix blocks, whose input and output singular vectors are the Fourier components of dimension equivalent to either number of actuators or number of measurements. This approximation enables the model predictive controller for these systems to be tuned by a numerical search over optimization weights in order to shape the closed-loop transfer functions in the two-dimensional frequency domain for performance and robustness. A real industrial multiple array CD process is used for illustrating the effectiveness of this method

Holographic spectral filter

Abstract: Method and apparatus are contemplated for receiving from an input, an optical signal in a volume hologram comprising a transfer function that may comprise temporal or spectral information, and spatial transformation information; diffracting the optical signal; and transmitting the diffracted optical signal to an output. A plurality of inputs and outputs may be coupled to the volume hologram. The transformation may be a linear superposition of transforms, with each transform acting on an input signal or on a component of an input signal. Each transform may act to focus one or more input signals to one or more output ports. A volume hologram may be made by various techniques, and from various materials. A transform function may be calculated by simulating the collision of a design input signal with a design output signal.

On the Selection of Spectral Zeros for Generating Passive Reduced Order Models

Abstract: As process technology continues to scale into the nanoscale regime, passive components and interconnect plays an ever increasing role in realization of mixed-signal systems. In this paper, the authors develop a new method for the model order reduction of passive components and interconnect using frequency selective projection methods with interpolation points based on the spectral-zeros of the RLC interconnect model's transfer function. The methodology uses imaginary part of the spectral zeros for frequency selective adaptive projection and provides stable as well as passive reduced order models. The results indicate that our method provides more accurate approximations than techniques based on balanced truncation and moment matching

A Proposed Stability Characterization and Verification Method for High-Order Single-Bit Delta-Sigma Modulators

Abstract: A characterization method for verifying stability and measuring the performance quality of arbitrary noise transfer functions for the delta-sigma modulator is presented The method consists of first obtaining the maximum stable input range sweep in the pass-band The variance estimate can then be used to make a sharper upper limit for maximum allowed input range This can then be used to measure the global SNR performance in the pass-band The proposed method enables us to make a comprehensive comparison between arbitrary noise transfer function designs and it can also be used to automate the design of noise transfer functions

Envelope-domain time series (ET) behavioral model of a Doherty RF power amplifier for system design

Abstract: In this paper, we present an envelope-domain behavioral model of a high-power RF amplifier. In this modeling approach, we use the signal envelope information, and the behavioral model is generated using an established nonlinear time-series approach to create a time-domain model that operates in the envelope or signal domain. We have generated a model of a 200-W Doherty amplifier from measured IQ data taken using a wideband code-division multiple-access excitation; the amplifier was driven from the linear regime into saturation. The time-series model was created using a time-delay embedding identified from auto-mutual information analysis, and an artificial neural network was used to fit the multivariate transfer function. The model has been validated using measured and simulated data, and it has been used in the development of a system-level design of a digital pre-distorter

On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers.

Abstract: We describe systematic measurements of the gain and delay spectra in a slow light system based on stimulated Brillouin scattering in optical fibers. The measurements yield the system complex transfer function with which delays and signal distortion can be calculated for any input signal. The theoretical predictions are confirmed experimentally for single pulses as well as 50 Mb/s data streams in a system which employs pump modulation to modify the gain and delay spectra of the SBS process.

Frequency Domain Analyses of SEATS and X-11/12-ARIMA Seasonal Adjustment Filters for Short and Moderate-Length Time Series

Abstract: We investigate frequency domain properties, revealed by the squared gain and phase delay functions, of short and moderate-length linear seasonal adjustment filters of the ARIMAmodel-based signal extraction method of SEATS. X-11/12-ARIMA filters are also considered to a limited extent. The focus is on the one-sided (concurrent) and symmetric (central) filters associated with the Box and Jenkins’s airline model for monthly time series of lengths 49 and 109. A Digital Signal Processing perspective on filter properties, favoring interpretability of the filter output, is presented. We show that important features of the finite filters actually used are often not visible in the diagnostics of the infinite filters, such as the Wiener-Kolmogorov symmetric filter gain functions provided by SEATS. For comparing competing adjustments, properties of concurrent filters, especially their phase delays, can be more important than properties of symmetric filters. Our phase delay results illustrate that adjusters who favor smoother seasonal adjustments, or who favor trends for their greater smoothness, must usually reckon with greater delay of turning point and business cycle information for the most recent months. Trend filters are considered briefly. New analytical results are obtained for transfer functions and phase delays.

A Bayesian geostatistical transfer function approach to tracer test analysis

Abstract: [1] Reactive transport modeling is often used in support of bioremediation and chemical treatment planning and design. There remains a pressing need for practical and efficient models that do not require (or assume attainable) the high level of characterization needed by complex numerical models. We focus on a linear systems or transfer function approach to the problem of reactive tracer transport in a heterogeneous saprolite aquifer. Transfer functions are obtained through the Bayesian geostatistical inverse method applied to tracer injection histories and breakthrough curves. We employ nonparametric transfer functions, which require minimal assumptions about shape and structure. The resulting flexibility empowers the data to determine the nature of the transfer function with minimal prior assumptions. Nonnegativity is enforced through a reflected Brownian motion stochastic model. The inverse method enables us to quantify uncertainty and to generate conditional realizations of the transfer function. Complex information about a hydrogeologic system is distilled into a relatively simple but rigorously obtained function that describes the transport behavior of the system between two wells. The resulting transfer functions are valuable in reactive transport models based on traveltime and streamline methods. The information contained in the data, particularly in the case of strong heterogeneity, is not overextended but is fully used. This is the first application of Bayesian geostatistical inversion to transfer functions in hydrogeology but the methodology can be extended to any linear system.

Parameter Estimation for Integrating Processes Using Relay Feedback Control under Static Load Disturbances

Abstract: Identifying the parameters of an assumed transfer function using the relay feedback control has become an accepted practical procedure. In process control problems, the transfer function may involve an integrator. Therefore, in this paper, a modified relay feedback control for parameter estimation of an integrating plus first-order plus dead time (IFOPDT) plant transfer function has been suggested, using the A-Function method, which is an exact method for investigating a limit cycle to occur. The effect of static load disturbances has been included in the derived expressions for a limit cycle to occur, so that better estimations can be performed under static load disturbances.

Decentralized Control System Design for Multivariable ProcessesA Novel Method Based on Effective Relative Gain Array

Abstract: In this paper, a novel method for design of a decentralized control system for multivariable processes is proposed. On the basis of a new interaction measure, effective relative gain array (ERGA), in terms of energy transmission ratio, loop interactions are quantified by two elements, i.e., relative gain and relative critical frequency. The interaction effects for a particular loop from all other closed loops are analyzed through both steady-state gain and critical frequency variations. Consequently, appropriate detuning factors for decentralized controllers under different interaction conditions can be derived based on the effective relative gain, relative gain, and relative critical frequency. The design method can be effectively used for both normal processes as well as process-loop transfer functions containing unstable zeros resulted from other closed loops. This design method is simple, straightforward, and effective and can be easily understood and implemented by field engineers. Several multivaria...

Stabilization of an arbitrary order transfer function with time delay using a PID controller

Abstract: This paper is concerned with developing a procedure for stabilizing a linear time-invariant plant of any order with time delay utilizing a proportional-integral-dervative (PID) controller. The method presented here is based on calculating the stability bounds in terms of the three planes (KP, K1), (Kp, Kd) and (KI, Kd), where Kp, Ki and Kd are proportional, integral and derivative gains, respectively. The advantage of this procedure is the fact that it does not require the knowledge of the plant transfer function parameters, but only its frequency response. In addition, if the plant function is known, the procedure may also be used to analytically obtain the stabilizing controllers. We also present the tuning rules for user specified gain and phase margins.

Analysis of the performance of a wireless optical multi-input to multi-output communication system

Abstract: We investigate robust optical wireless communication in a highly scattering propagation medium using multielement optical detector arrays. The communication setup consists of synchronized multiple transmitters that send information to a receiver array and an atmospheric propagation channel. The mathematical model that best describes this scenario is multi-input to multi-output communication through stochastic slow changing channels. In this model, signals from m transmitters are received by n receiver-detectors. The channel transfer function matrix is G, and its size is n x m. G(i,j) is the transfer function from transmitter i to detector j, and m > or = n. We adopt a quasi-stationary approach in which the channel time variation has a negligible effect on communication performance over a burst. The G matrix is calculated on the basis of the optical transfer function of the atmospheric channel (composed of aerosol and turbulence elements) and the receiver's optics. In this work we derive a performance model using environmental data, such as documented turbulence and aerosol models and noise statistics. We also present the results of simulations conducted for the proposed detection algorithm.