Analytical Design and Polyphase Implementation Technique for 2D Digital FIR Differentiators

In this work, an analytical method in the frequency domain is proposed for the design of two-dimensional digital FIR differentiators. This technique uses an approximation based on two methods: the Chebyshev series and the Fourier series, which, finally, lead to a trigonometric polynomial, which is a remarkably precise approximation of the transfer function of the ideal differentiator. The digital differentiator is applied to three test images, one greyscale image and two binary images, and simulation results show its performance in the processing task. Also, based on the fact that this 2D differentiator is separable on the two frequency axes, we propose an efficient implementation at the system level, using polyphase filtering. The designed digital differentiator is very accurate and efficient, having a high level of parallelism and reduced computational complexity.