Fractional Step Low-Pass Filters Realization Using Switched-Current Circuit and Modified Teaching-Learning-Based Optimization Algorithm

A method of switched-current (SI) fractional step filter (FSF) implementation of low-pass filter prototype with Butterworth characteristics based on modified Teaching-Learning-Based optimization (MTLBO) algorithm was presented in this work. Firstly, fractional order Laplacian operator $s_{\\alpha}$ (0<α<1) was approximated by an integer order function using continued fraction expansions (CFE) method. Then the FSF of order (1+α) was approximated using the MTLBO algorithm in order to improve the approximation accuracy. Secondly, the SI fractional step low-pass filters (FSLF) of orders 1.1, 1.5 and 1.9 with the Follow-the-Leader Feedback (FLF) structure was designed using the SI bilinear lossless integrator as the basic block. Finally, the implementation method of the FSF is verified through Matlab simulations and experimentation.