Optimal Design of Two-Dimensional Fractional-Order Riesz Digital Differentiator

This study examines the design considerations of the 2-dimensional fractional-order Riesz digital differentiator (FORDD). The initial task entails the creation of a 2-dimensional fractional-order digital differentiator (FODD) utilizing a 2-D discrete cosine transform (DCT). Then, it is demonstrated that the frequency response of the 2-dimensional fractional-order Riesz digital differentiator (FORDD) is only the scaling even part of the 2-dimensional conventional FODD frequency response. The design example demonstrates the use of 2-D DCT to assess the effectiveness of the suggested 2-dimensional fractional-order Riesz digital differentiator (FORDD). The outcomes of the simulation illustrate that the proposed 2-dimensional FORDD is more effective than the existing 2-dimensional fractional-order digital differentiator (FODD) which has 0.0395 of average magnitude error and 439.89 seconds of execution time.