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.

Analytic Design Technique for 2D FIR Circular Filter Banks and Their Efficient Implementation Using Polyphase Approach.

This paper proposes an analytical design procedure for 2D FIR circular filter banks and also a novel, computationally efficient implementation of the designed filter bank based on a polyphase structure and a block filtering approach. The component filters of the bank are designed in the frequency domain using a specific frequency transformation applied to a low-pass, band-pass and high-pass 1D prototype with a specified Gaussian shape and imposed specifications (peak frequency, bandwidth). The 1D prototype filter frequency response is derived in a closed form as a trigonometric polynomial with a specified order using Fourier series, and then it is factored.