In the last ten years, the traditional Simpson quadrature rule for numerical integration has been improved to an optimal 3-point quadrature formula and a modified Simpson rule that takes additionally the first derivative of the approximated integrand at the two end-points of integration into account. The impact of the improved quadrature rules on the fast Fourier transform (FFT) approximation o...

A new IIR (infinite impulse response) type digital fractional order differentiator (DFOD) is proposed by using a new family of first order digital differentiators expressed in the second order IIR filter form. The integer first order digital differentiators are obtained by the stable inversion of the weighted sum of Simpson integration rule and the trapezoidal integration rule. The distinguishi...

Steve Simpson was born and grew up in Australia. After completing his undergraduate degree at the University of Queensland, he travelled to London where he undertook his PhD on locust feeding physiology. Steve then spent 22 years in Oxford, fi rst in Experimental Psychology and then in the Department of Zoology and the Natural History Museum, before being enticed back to Australia in 2005. Toge...