Analytical Design and Efficient Systolic Polyphase Implementation for 2D Gaussian Circular FIR Filters
Doru Florin Chiper, Radu P. Matei, Paul Ungureanu, Adrian Popa · 2025
This paper presents an analytical design method in the frequency domain for a class of 2D separable FIR filters, with a circular low-pass frequency response, based on a Gaussian prototype with specified bandwidth. The ideal Gaussian response is approximated by a trigonometric polynomial through a Fourier series expansion of order 15, ensuring a smooth approximation with a low level of distortion even for narrow band fiters. By an appropriate reformulation of the basic equation of a separable 2D FIR filter we get an efficient systolic implementation based on a hardware accelerator, used together with the host computer to accelerate the computation of 2D FIR filtering. Using a polyphase decomposition, the VLSI implementation that computes a$5 \times 52 \mathrm{D}$FIR filter can be extended to a 2D FIR filter with a$15 \times 15$kernel. Through an appropriate reformulation of the basic form of the 2 D FIR filter, it was possible to compute four terms of the final equation using the same hardware accelerator. Thus, an efficient, high-speed implementation of the 2D FIR filter has been obtained.