Carathéodory–Toeplitz based mathematical methods and their algorithmic applications in biometric image processing

2017

Summary This paper is concerned with the realization problem for a class of high‐pass as well as low‐pass transfer functions as a two‐port RC ladder network with a specified gain, which requires that the actual gain of the realization configuration is equal to the gain of the given transfer function. From a cascade realization approach, it is shown that any transfer function belonging to the class under investigation can be realized as a two‐port RC ladder network with any specified gain in a continuous interval. Finally, a numerical example is presented to illustrate the result. Copyright © 2017 John Wiley & Sons, Ltd.

Section: Introductionmentioning

confidence: 99%

Realization of a transfer function as a passive two‐port RC ladder network with a specified gain

2017

“…In (, Section 5), the realizability conditions of a biquadratic impedance with at most four elements are utilized to optimize the performances of vehicle suspension systems containing passive mechanical network struts and mechatronic network struts, respectively. Besides mechanical systems control, synthesis of passive networks can also be applied to a series of other fields, such as the microwave circuit design , filter deign , biometric image processing , model reduction preserving passivity , and open and interconnected systems . Particularly, an independent call for renewed effort has been made by Kalman .…”

Section: Introductionmentioning

confidence: 99%

A generalized theorem of Reichert for biquadratic minimum functions

Zou

2016

SUMMARYThis paper is concerned with a generalized theorem of Reichert for biquadratic minimum functions, which states that any biquadratic minimum function realizable as the impedance of networks with n reactive elements and an arbitrary number of resistors can be realized with n reactive elements and two resistors. First, a series of constraints on networks realizing minimum functions are presented. Furthermore, by discussing the possible resistor edges incident with vertices of the reactive-element graphs, it is proved that any minimum function realizable as the impedance of networks with three reactive elements and an arbitrary number of resistors can be realized with three reactive elements and two resistors, from which the validity of the case of n = 3 follows. Similarly, the validity of the case of n = 4 is proved. Together with the Bott-Duffin realizations, the generalized theorem of Reichert for biquadratic minimum functions is finally proved. The results of this paper are motivated by passive mechanical control.

“…Lately, interest in passive network synthesis has been renewed . The results in have also been applied to approximate realization of fractional‐order 2‐D IIR frequency‐planar filters and biometric image processing . In particular, there was an independent call for a renewed investigation of the subject by Kalman .…”

Section: Introductionmentioning

confidence: 99%

Synthesis of n‐port resistive networks containing 2n terminals

et al. 2013

This paper is concerned with the realizability problem of n‐port resistive networks that contain 2n terminals. A necessary and sufficient condition for any real symmetric matrix to be realizable as the admittance of an n‐port resistive network containing 2n terminals is obtained. This condition is based on the existence of a parameter matrix. Furthermore, the values of the elements are expressed in terms of the entries of the admittance matrix and the parameter matrix. Finally, a numerical example is used to illustrate the results. Copyright © 2013 John Wiley & Sons, Ltd.