Premium
General rational approximation of Gaussian wavelet series and continuous‐time g m ‐C filter implementation
Author(s) -
Li Mu,
Sun Yichuang
Publication year - 2020
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2834
Subject(s) - wavelet , cascade algorithm , wavelet packet decomposition , mathematics , gaussian filter , wavelet transform , stationary wavelet transform , gaussian , algorithm , discrete wavelet transform , filter design , second generation wavelet transform , legendre wavelet , filter (signal processing) , control theory (sociology) , computer science , physics , artificial intelligence , control (management) , quantum mechanics , computer vision
Summary A general method of rational approximation for Gaussian wavelet series and Gaussian wavelet filter circuit design with simple g m ‐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 g m ‐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.