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.

Spatial-domain design of two-dimensional recursive digital filters

Abstract: A technique using linear algebraic projection is proposed to design two-dimensional (2-D) recursive digital filters that best approximate a desired input/output relationship in terms of total weighted squared error. A 2-D difference equation representation is used. Examples of first-quadrant and asymmetric half-plane filters are presented and compared with other spatial-domain designs. One of the main advantages of the proposed method is that the solution is obtained directly with no need for iterations. >

On the simplification of linear systems

Abstract: This note presents a method for approximating a high-order linear-system transfer function by a low-order model. The method developed is based on the requirement that the magnitude ratio of the frequency responses of the model and the original system deviate the least at various frequencies. In selecting the order and structure of the model, one has the flexibility of prefixing certain poles and zeros in the model transfer function.

Design and Analysis of Sliding Mode Controller Under Approximate Hysteresis Compensation

Abstract: A sliding mode controller (SMC) is proposed for a class of systems comprising a hysteresis operator preceding a linear system with an all-pole transfer function. The hysteresis operator is modeled with uncertain piecewise linear characteristics, and a nominal inverse operator is included to mitigate the hysteresis effect. A classical SMC design typically uses a constant coefficient in the switching component, which is tuned via trial-and-error. In this paper, a state- and time-dependent coefficient is proposed based on the derived inversion error, which eliminates the need for parameter tuning and ensures the convergence of the sliding surface to the boundary layer without compactness assumptions. In addition, singular perturbation is used to analyze the system behavior within the sliding-surface boundary layer for the case of a constant coefficient in the classical SMC design. In particular, analytical insight is gained on the frequency-scaling behavior of the tracking error under a periodic reference. Simulation and experimental results based on a piezoelectric actuator-based nanopositioner are presented to illustrate the design and analysis, where the hysteresis nonlinearity is represented by a Prandtal-Ishlinskii operator.

Bifrequency and bispectrum maps: a new look at multirate systems with stochastic inputs

Abstract: In multirate digital signal processing, we often encounter decimators, interpolators, and complicated interconnections of these with LTI filters. We also encounter cyclo-wide-sense stationary (CWSS) processes and linear periodically time-varying (PTV) systems. It is often necessary to understand the effects of multirate systems on the statistical properties of their input signals. Some of these issues have been addressed earlier. For example, it has been shown that a necessary and sufficient addition for the output of an L-fold interpolation filter to be wide sense stationary (WSS) for all WSS inputs is that the filter was an alias-free (L) support. However, several questions of this nature remain unanswered. For example, what is the necessary and sufficient condition on a pair (or more generally a bank) of interpolation filters so that their outputs are jointly WSS (JWSS) for all jointly WSS inputs? What is the condition if only the sum of their outputs is required to be WSS? When is the output of an LPTV system (for example a uniform filter-bank) WSS for all WSS inputs? Some of these questions may appear to be simple generalizations of the above-mentioned result for a single interpolation filter. However, the frequency domain approaches that proved this result are quite difficult to generalize to answer these questions. The purpose of this paper is to provide these answers using analysis based on bifrequency maps and bispectra. These tools are two-dimensional (2-D) Fourier transforms that characterize linear time-varying (LTV) systems and nonstationary random processes, respectively. We show that the questions raised above are addressed elegantly and in a geometrically insightful way using these tools. We also derive a bifrequency characterization lossless LTV systems. This may potentially lead to an increased understanding of these systems.