Fractional Bilinear Transform for Analog-to-Digital Conversion

In this correspondence, we propose a fractional bilinear transform used in analog-to-digital (A/D) conversion. This transfer function is derived by means of fractional delay filters. According to this transformation, first-order differentiator can be easily designed. Next, some design examples are illustrated to show the linear frequency mapping property when doing A/D conversion. Finally, the designed low-order digital differentiator is compared with the existing differentiators.