Transfer Function Framework Research Articles

High-resolution microscopic fringe projection profilometry using Nyquist frequency fringe

Vertical resolution is a crucial property in microscopic fringe projection profilometry (MFPP) systems. The challenge in improving vertical resolution lies not only in enhancing height-sensing sensitivity but also in reducing the gain of phase-shifting algorithms (PSA) against dominant noise in the fringe signal. This study uses an optical flat for continuous phase shifting, achieving phase demodulation for fringe with Nyquist frequency. To mitigate the inherent disturbances caused by continuous phase shifting during phase demodulation, a transfer relation between phase-shift error and 1/f noise is established using spectral analysis and the frequency transfer function framework. Based on this transfer relation, we propose a novel PSA with high signal noise ratio and sensitivity. Experiments validate the proposed PSA, indicating that the vertical resolution of a telecentric MFPP system using the proposed PSA is 73 nm. The reconstruction results of wafer-level 3D structures are consistent with those from confocal microscopy.

Adaptation of the visibility graph algorithm for detecting time lag between rainfall and water level fluctuations in Lake Okeechobee

Identifying time-lag between two hydrogeological time series for planning and management of water resources has a long history and is of continuing research interest. Many hydrogeological studies in the past have used visual inspection and cross-correlogram techniques for quantifying the time lag. Cross-correlogram techniques, if not done under the transfer function framework, could lead to ambiguous results. In order to conduct cross-correlogram analysis under the transfer function framework, careful pre-processing steps have to be undertaken, which are often ignored in practice. In this paper, we propose a new approach to compare two sets of hydrogeological time series data using the visibility graph algorithm and show the advantages of using the new approach over the traditional approach. Application of the new approach is demonstrated by assessing the lags between rainfall and water level fluctuation in Lake Okeechobee, Florida. We also present simulation studies to better understand the performance of the method for different sample sizes, different underlying models and in the presence of missing values.

Box-Jenkins transfer function framework applied to saving-investment nexus in the South African context

This paper studied the relationship between investment and savings in South Africa for the period 1990 quarter 1 to 2014 quarter 3. The unit root test confirmed the non-stationarity of the series prior to first differencing. The correlation coefficient and the model assessing a full capacity mobility hypothesis were significant and passed all the diagnostic examinations. The estimated parameter provided evidence of imperfect capital mobility. ARIMAX (5, 1, 0) out-performed all the five models and was used for pre-whitening process. This model was later used to produce a two year forecasts of investment. The error forecast measure provided enough evidence to conclude that ARIMAX (5, 1, 0) provided valid forecasts. These results are recommended when embarking on future saving-investment plans in South Africa.

Modeling of micro-perforated panels in a complex vibro-acoustic environment using patch transfer function approach

A micro-perforated panel (MPP) with a backing cavity is a well known device for efficient noise absorption. This configuration has been thoroughly studied in the experimental conditions of an acoustic tube (Kundt tube), in which the MPP is excited by a normal incident plane wave in one dimension. In a more practical situation, the efficiency of MPP may be influenced by the vibro-acoustic behavior of the surrounding systems as well as excitation. To deal with this problem, a vibro-acoustic formulation based on the patch transfer functions (PTF) approach is proposed to model the behavior of a micro-perforated structure in a complex vibro-acoustic environment. PTF is a substructuring approach, which allows assembling different vibro-acoustic subsystems through coupled surfaces. Upon casting micro-perforations and the flexibility of the MPP under transfer function framework, the proposed PTF formulation provides explicit representation of the coupling between subsystems and facilitates physical interpretation. As an illustration example, application to a MPP with a backing cavity located in an infinite baffle is demonstrated. The proposed PTF formulation is finally validated through comparison with experimental measurements available in the literature.

An empirical model of daily highs and lows of West Texas Intermediate crude oil prices

There is a large collection of literature on energy price forecasting, but most studies typically use monthly average or close-to-close daily price data. In practice, the daily price range constructed from the daily high and low also contains useful information on price volatility and is used frequently in technical analysis. The interaction between the daily high and low and the associated daily range has been examined in several recent studies on stock price and exchange rate forecasts. The present paper adopts a similar approach to analyze the behaviour of the West Texas Intermediate (WTI) crude oil price over a ten-year period. We find that daily highs and lows of the WTI oil price are cointegrated, with the error correction term being closely approximated by the daily price range. Two forecasting models, one based on a vector error correction mechanism and the other based on a transfer function framework with the range taken as a driver variable, are presented for forecasting the daily highs and lows. The results show that both of these models offer significant advantages over the naïve random walk and univariate ARIMA models in terms of out-of-sample forecast accuracy. A trading strategy that makes use of the daily high and low forecasts is further developed. It is found that this strategy generally yields very reasonable trading returns over an evaluation period of about two years.

A numerically robust state-space approach to stable-predictive control strategies

Recent work with predictive control strategies has shown that the stable GPC (SGPC) approach has significant computational and numerical advantages. However, SGPC is cast in the transfer function framework which limits its application. Here we develop a means of extending the results to state-space models and show that improved numerical conditioning can be obtained for many stable-predictive control strategies.

A Transfer-Function Approach to Linear Time-Varying Discrete-Time Systems

In the first part of the paper a transfer-function approach is developed for the class of linear time-varying discrete-time systems. The theory is specified in terms of skew (noncommutative) rings of polynomials and formal power series, both with coefficients in a ring of time functions. The transfer-function matrix is defined to be a matrix whose entries belong to a skew ring of formal power series. It is shown that various system properties, such as asymptotic stability, can be characterized in terms of the skew-ring framework. In the last part of the paper, the transfer-function framework is applied to the study of feedback control. New results are obtained on assignability of system dynamics by using dynamic output feedback and dynamic state feedback. The results are applied to the control of an armature-controlled do motor with a variable loading.