Design of a class of fractional-order analog wavelet filters

In this article, a methodology is proposed to implement fractional-order analog wavelet filters in the frequency domain. Under the proposed scheme, the fractional-order transfer function of the linear time-invariant system is used to approximate the Gaussian-like wavelet functions. Firstly, we construct a causal, stable, and physically achievable fractional-order mathematical approximation model. Then, the fractional-order mathematical approximation model is transformed into an optimization problem, and a hybrid particle swarm optimization algorithm is exploited to find its global optimal solution. At the same time, constraint terms are introduced to ensure the desired stability. The simulation results show that the fractional-order analog wavelet filters have higher approximation accuracy than the traditional integer-order analog wavelet filters. Furthermore, fractional-order analog wavelet filters can provide more precise control of the stopband attenuation rate, which is a key issue for many engineering applications.