Transfer function

About: Transfer function is a research topic. Over the lifetime, 14362 publications have been published within this topic receiving 214983 citations. The topic is also known as: system function & network function.

Resolving spectral information from time domain induced polarization data through 2-D inversion

Abstract: SUMMARY Field-basedtimedomain(TD)inducedpolarization(IP)surveysareusuallymodelledbytaking into account only the integral chargeability, thus disregarding spectral content. Furthermore, the effect of the transmitted waveform is commonly neglected, biasing inversion results. Given these limitations of conventional approaches, a new 2-D inversion algorithm has been developed using the full voltage decay of the IP response, together with an accurate description of the transmitter waveform and receiver transfer function. This allows reconstruction of the spectral information contained in the TD decay series. The inversion algorithm is based around a 2-D complex conductivity kernel that is computedoverarangeoffrequenciesandconvertedtotheTDthroughafastHankeltransform. Two key points in the implementation ensure that computation times are minimized. First, the speed of the Jacobian computation, time transformed from frequency domain through the same transformation adopted for the forward response is optimized. Secondly, the reduction of the number of frequencies where the forward response and Jacobian are calculated: cubic splines are used to interpolate the responses to the frequency sampling necessary in the fast Hankel transform. These features, together with parallel computation, ensure inversion times comparable with those of direct current algorithms. Thealgorithmhasbeendevelopedinalaterallyconstrainedinversionscheme,andhandles both smooth and layered inversions; the latter being helpful in sedimentary environments, where quasi-layered models often represent the actual geology more accurately than smooth minimum-structure models. In the layered inversion approach, a general method to derive the thickness derivative from the complex conductivity Jacobian is also proposed. One synthetic example of layered inversion and one field example of smooth inversion show the capability of the algorithm and illustrates a complete uncertainty analysis of the model parameters. With this new algorithm, in situ TD IP measurements give access to the spectral content of the polarization processes, opening up new applications in environmental and hydrogeophysical investigations.

Evaluation of an algorithm for the assessment of the MTF using an edge method.

Abstract: An algorithm to calculate the presampling modulation transfer function (MTF) of an imaging system from an angled edge image has its own inherent transfer function. Factors such as the angle of the sampling aperture to the edge, registration of edge function profiles using the determined edge angle, differentiation, smoothing, and folding all combine to produce the frequency response of the algorithm. In this work, the profile registration transfer function accounting for an error in the determined edge angle has been derived. This has been incorporated with other, previously reported, algorithm component transfer functions to fully characterize the MTF calculation algorithm. When registering profiles, small errors in the edge angle determination were found to result in large errors in the MTF, as the misalignment errors increase with the number of profiles. For example, registering 50 profiles a 0.07 degree error in a 7 degree edge angle (1% error) produces a 36% error in the MTF at the system cutoff frequency f=f(c) when profiles are oversampled at a frequency f(s)=8f(c)(f(c) is defined as the maximum frequency reproducible without aliasing when sampling at the limiting system Nyquist frequency f(s) = 2f(c)). These results highlight the importance of quantifying the transfer function of the algorithm used to determine an imaging system modulation transfer function. The MTF calculation algorithm and the transfer function analysis have been incorporated into a Windows-based software program to be made available for general use.

A general transfer function approach to linear stationary filtering and steady-state optimal control problems

Abstract: The transfer-function form of the stationary algebraic Riccati equation is investigated. A generalized spectral factorization technique that copes with unstable systems is introduced. This factorization is used to provide an efficient way of solving the Riccati equation and to establish the exact equivalence between the time domain and the transfer-function approaches to the linear stationary filtering and the deterministic optimal control problems. The proposed method is easily extended to cope, in the filtering problem, with coloured signals and the superiority of its computational method for systems having a small number of inputs and outputs is demonstrated. Finally, an application of the transfer-function approach in determining the class of all systems that share the same optimal solution is introduced.

An analytical edge spread function model for computer fitting and subsequent calculation of the LSF and MTF

Abstract: The previous work of Yin, Giger, and Doi [Med. Phys. 17, 962-966 (1990)] demonstrated that using a computerized fit of an analytic line spread function to experimentally measured data is very useful for determining the presampling modulation transfer function of an imaging system. In this report, the work of Yin et al. is extended to include an analytic expression for the edge spread function (ESF). By fitting experimentally determined edge spread function data to the analytical expression, the normalized line spread function (LSF) and the normalized modulation transfer function (MTF) can be easily calculated from four ESF fit coefficients. The extension from the line spread function to the edge spread function should be valuable in cases where slit measurements are impractical, for example, in very high resolution imaging systems where the required slit dimensions become impractically small, or in measurements of the transfer properties of scattered radiation or off-focus radiation, where large area exposures are necessary.

Small-signal analysis of frequency-controlled electronic ballasts

Abstract: This paper presents analytical tools aimed at improving and simplifying the development of frequency-controlled dimming electronic ballasts. A modified phasor transformation is proposed that converts a frequency-modulated signal into an equivalent time-varying phasor. The proposed transformation is applied to develop a complete small-signal phasor model of the LCC resonant ballast, which explicitly models the effect of the frequency modulation on the envelopes of the outputs. A Spice-compatible implementation of the model is presented that facilitates ac analysis of the ballast in addition to envelope transient simulation, and is verified through comparison of experimental and simulation results. A closed-form solution of the control-to-output current transfer function for the ballast-resistor system is presented, along with key observations of the pole locations and low-frequency gain that facilitate simple and intuitive compensator design. The effects of lamp dynamics on the controller design are discussed, followed by a design example for the feedback controller.