Brief Historical Introduction

Summary A general method of rational approximation for Gaussian wavelet series and Gaussian wavelet filter circuit design with simple gm‐C integrators is presented in this work. Firstly, the multiorder derivatives of Gaussian function are analyzed and proved as wavelet base functions. Then a high‐accuracy general approximation model of Gaussian wavelet series is constructed, and the transfer function of first‐order derivative of Gaussian wavelet filter is obtained using quantum differential evolution (QDE) algorithm. Thirdly, as an example, a fifth‐order continuous‐time analog first‐order derivative of Gaussian wavelet filter circuit is designed based on multiple loop feedback structure with a simple gm‐C integrator as the basic blocks. Finally, simulation results demonstrate that the proposed method is an excellent way for the wavelet transform implementation. The designed first‐order derivative of Gaussian wavelet filter circuit operates from a 0.53‐V supply voltage and a bias current 2.5 nA. The power dissipation of the wavelet filter circuit at the basic scale is 41.1 nW. Moreover, the high‐accuracy QRS detection based on the designed wavelet filter has been validated in application analysis.

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Generalized wavelet quasilinearization method for solving population growth model of fractional order

Srivástava

Shah

Irfan

2020

Math Methods in App Sciences

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The primary aim of this study is to introduce and develop a generalized wavelet method together with the quasilinearization technique to solve the Volterra's population growth model of fractional order. Unlike the existing operational matrix methods based on orthogonal functions, we formulate the wavelet operational matrices of general order integration without using the block pulse functions. Consequently, the governing problem is transformed into an equivalent system of algebraic equations, which can be tackled with any classical method. The applicability of the proposed method is demonstrated via an illustrative comparison of the numerical outcomes with those found by other known methods. The experimental outcomes demonstrate that the proposed method is fast, accurate, simple, and computationally reliable.

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Brief Historical Introduction

Cited by 10 publications

References 37 publications

A computational wavelet method for solving dual‐phase‐lag model of bioheat transfer during hyperthermia treatment

A computational wavelet method for solving dual‐phase‐lag model of bioheat transfer during hyperthermia treatment

General rational approximation of Gaussian wavelet series and continuous‐timeg_m‐C filter implementation

Generalized wavelet quasilinearization method for solving population growth model of fractional order

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Brief Historical Introduction

Cited by 10 publications

References 37 publications

A computational wavelet method for solving dual‐phase‐lag model of bioheat transfer during hyperthermia treatment

A computational wavelet method for solving dual‐phase‐lag model of bioheat transfer during hyperthermia treatment

General rational approximation of Gaussian wavelet series and continuous‐timegm‐C filter implementation

Generalized wavelet quasilinearization method for solving population growth model of fractional order

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Product

Resources

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General rational approximation of Gaussian wavelet series and continuous‐timeg_m‐C filter implementation