<p>The design of digital fractional-delay filters involves complex mathematical operations and numerical approximations. This paper presents the design of a general digital fractional-delay IIR filter using the composite function rule. The aim is to enhance the design accuracy of the conventional fractional delay design method in high-frequency areas. The proposed approach is based on the Charef approximation method of the analog fractional order systems. First, the rational analog approximation is converted to digital using the Bilinear-Tustin transformation. Next, the composite function is applied to the digital approximation to approximate the ideal digital fractional delay operator z^−m. Then, a parallel realization of digital IIR fractional delay filters is used to design the proposed filter structure. Finally, we demonstrate the effectiveness of the proposed approach using various numerical examples and emphasize its versatility in designing some practical filters.</p>