Analysis of a linear one-dimensional active noise control system by means of block diagrams and transfer functions

In arriving at the ideal filter transfer function for an active noise control system in a duct, the effect of the auxiliary sources (generally loudspeakers) on the waves generated by the primary source has invariably been neglected in the existing literature, implying a rigid wall or infinite impedance. The present paper presents a fairly general analysis of a linear one-dimensional noise control system by means of block diagrams and transfer functions. It takes into account the passive as well as active role of a terminal primary source, wall-mounted auxiliary source, open duct radiation impedance, and the effects of mean flow and damping. It is proved that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against an anechoic termination and the other by reflecting the rearward wave (incident on the source) off the passive source impedance. Application of this concept is illustrated for both the types of sources. A concise closed-form expression for the ideal filter transfer function is thus derived and discussed. Finally, the dynamics of an adaptive noise control system is discussed briefly, relating its standing-wave variables and transfer functions with those of the progressive-wave model presented here.

Nonlinear dynamic transfer functions for certain retinal neuronal systems

The applicability of the white-noise method to the identification of a nonlinear system is investigated. Subsequently, the method is applied to certain vertebrate retinal neuronal systems and nonlinear, dynamic transfer functions are derived which describe quantitatively the information transformations starting with the light-pattern stimulus and culminating in the ganglion response which constitutes the visually-derived input to the brain. The retina of the catfish, Ictalurus punctatus, is used for the experiments.

The Wiener formulation of the white-noise theory is shown to be impractical and difficult to apply to a physical system. A different formulation based on crosscorrelation techniques is shown to be applicable to a wide range of physical systems provided certain considerations are taken into account. These considerations include the time-invariancy of the system, an optimum choice of the white-noise input bandwidth, nonlinearities that allow a representation in terms of a small number of characterizing kernels, the memory of the system and the temporal length of the characterizing experiment. Error analysis of the kernel estimates is made taking into account various sources of error such as noise at the input and output, bandwidth of white-noise input and the truncation of the gaussian by the apparatus.

Nonlinear transfer functions are obtained, as sets of kernels, for several neuronal systems: Light → Receptors, Light → Horizontal, Horizontal → Ganglion, Light → Ganglion and Light → ERG. The derived models can predict, with reasonable accuracy, the system response to any input. Comparison of model and physical system performance showed close agreement for a great number of tests, the most stringent of which is comparison of their responses to a white-noise input. Other tests include step and sine responses and power spectra.

Many functional traits are revealed by these models. Some are: (a) the receptor and horizontal cell systems are nearly linear (small signal) with certain "small" nonlinearities, and become faster (latency-wise and frequency-response-wise) at higher intensity levels, (b) all ganglion systems are nonlinear (half-wave rectification), (c) the receptive field center to ganglion system is slower (latency-wise and frequency-response-wise) than the periphery to ganglion system, (d) the lateral (eccentric) ganglion systems are just as fast (latency and frequency response) as the concentric ones, (e) (bipolar response) = (input from receptors) - (input from horizontal cell), (f) receptive field center and periphery exert an antagonistic influence on the ganglion response, (g) implications about the origin of ERG, and many others.

An analytical solution is obtained for the spatial distribution of potential in the S-space, which fits very well experimental data. Different synaptic mechanisms of excitation for the external and internal horizontal cells are implied.

A comparison of diatom phosphorus transfer functions and export coefficient models as tools for reconstructing lake nutrient histories

1. We compared the baseline phosphorus (P) concentrations inferred by diatom-P transfer functions and export coefficient models at 62 lakes in Great Britain to assess whether the techniques produce similar estimates of historical nutrient status. 2. There was a strong linear relationship between the two sets of values over the whole total P (TP) gradient (2-200 mu g TP L-1). However, a systematic bias was observed with the diatom model producing the higher values in 46 lakes (of which values differed by more than 10 mu g TP L-1 in 21). The export coefficient model gave the higher values in 10 lakes (of which the values differed by more than 10 mu g TP L-1 in only 4). 3. The difference between baseline and present-day TP concentrations was calculated to compare the extent of eutrophication inferred by the two sets of model output. There was generally poor agreement between the amounts of change estimated by the two approaches. The discrepancy in both the baseline values and the degree of change inferred by the models was greatest in the shallow and more productive sites. 4. Both approaches were applied to two lakes in the English Lake District where long-term P data exist, to assess how well the models track measured P concentrations since approximately 1850. There was good agreement between the pre-enrichment TP concentrations generated by the models. The diatom model paralleled the steeper rise in maximum soluble reactive P (SRP) more closely than the gradual increase in annual mean TP in both lakes. The export coefficient model produced a closer fit to observed annual mean TP concentrations for both sites, tracking the changes in total external nutrient loading. 5. A combined approach is recommended, with the diatom model employed to reflect the nature and timing of the in-lake response to changes in nutrient loading, and the export coefficient model used to establish the origins and extent of changes in the external load and to assess potential reduction in loading under different management scenarios. 6. However, caution must be exercised when applying these models to shallow lakes where the export coefficient model TP estimate will not include internal P loading from lake sediments and where the diatom TP inferences may over-estimate TP concentrations because of the high abundance of benthic taxa, many of which are poor indicators of trophic state.

Identification of fractional-order transfer functions using a step excitation

This brief proposes a new method for the identification of fractional order transfer functions based on the time response resulting from a single step excitation. The proposed method is applied to the identification of a three-dimensional RC network, which can be tailored in terms of topology and composition to emulate real time systems governed by fractional order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined, demonstrating that the fractional order modelling approach leads to very parsimonious model formulations.

On Complementary Root Locus of Biproper Transfer Functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Kinetic aspects of ion exchange in KhFek[Fe(CN)(6)](l)center dot mH(2)O compounds: A combined electrical and mass transfer functions approach

The present paper quantifies and develops the kinetic aspects involved in the mechanism of interplay between electron and ions presented elsewhere(1) for KhFek[Fe(CN)(6)](l)center dot mH(2)O (Prussian Blue) host materials. Accordingly, there are three different electrochemical processes involved in the PB host materials: H3O+, K+, and H+ insertion/extraction mechanisms which here were fully kinetically studied by means of the use of combined electronic and mass transfer functions as a tool to separate all the processes. The use of combined electronic and mass transfer functions was very important to validate and confirm the proposed mechanism. This mechanism allows the electrochemical and chemical processes involved in the KhFek[Fe(CN)(6)](l)center dot mH(2)O host and Prussian Blue derivatives to be understood. In addition, a formalism was also developed to consider superficial oxygen reduction. From the analysis of the kinetic processes involved in the model, it was possible to demonstrate that the processes associated with K+ and H+ exchanges are reversible whereas the H3O+ insertion process was shown not to present a reversible pattern. This irreversible pattern is very peculiar and was shown to be related to the catalytic proton reduction reaction. Furthermore, from the model, it was possible to calculate the number density of available sites for each intercalation/deintercalation processes and infer that they are very similar for K+ and H+. Hence, the high prominence of the K+ exchange observed in the voltammetric responses has a kinetic origin and is not related to the amount of sites available for intercalation/deintercalation of the ions.

Teaching general concepts about sensors and transfer functions with a voltage divider

This work proposes the use of a simple voltage divider circuit composed by one potentiometer and one resistor to simulate the behavior of the electrical output signal of linear and nonlinear sensors. It is a low cost way to implement practical experiments in classroom and it also enables the analysis of interesting topics of electricity. This work induces naturally to a class guide where students can build and characterize a voltage divider to explore several concepts about sensors output signal. As the result of this teaching activity it is expected that students understand fundamentals of voltage divider, potentiometer operation, fundamental sensor characteristics, transfer function, and, besides, associate directly concepts of physics and mathematics with a practical approach.

Transfer Functions in Artificial Neural Networks - A Simulation-Based Tutorial

Artificial neural networks are based on computational units that resemble basic information processing properties of biological neurons in an abstract and simplified manner. Generally, these formal neurons model an input-output behaviour as it is also often used to characterize biological neurons. The neuron is treated as a black box; spatial extension and temporal dynamics present in biological neurons are most often neglected. Even though artificial neurons are simplified, they can show a variety of input-output relations, depending on the transfer functions they apply. This unit on transfer functions provides an overview of different transfer functions and offers a simulation that visualizes the input-output behaviour of an artificial neuron depending on the specific combination of transfer functions.

The performance of single- and multi-proxy transfer functions (testate amoebae, bryophytes, vascular plants) for reconstructing mire surface wetness and pH

Peatlands are widely exploited archives of paleoenvironmental change. We developed and compared multiple transfer functions to infer peatland depth to the water table (DWT) and pH based on testate amoeba (percentages, or presence/absence), bryophyte presence/absence, and vascular plant presence/absence data from sub-alpine peatlands in the SE Swiss Alps in order to 1) compare the performance of single-proxy vs. multi-proxy models and 2) assess the performance of presence/absence models. Bootstrapping cross-validation showing the best performing single-proxy transfer functions for both DWT and pH were those based on bryophytes. The best performing transfer functions overall for DWT were those based on combined testate amoebae percentages, bryophytes and vascular plants; and, for pH, those based on testate amoebae and bryophytes. The comparison of DWT and pH inferred from testate amoeba percentages and presence/absence data showed similar general patterns but differences in the magnitude and timing of some shifts. These results show new directions for paleoenvironmental research, 1) suggesting that it is possible to build good-performing transfer functions using presence/absence data, although with some loss of accuracy, and 2) supporting the idea that multi-proxy inference models may improve paleoecological reconstruction. The performance of multi-proxy and single-proxy transfer functions should be further compared in paleoecological data.