Design of cost effective variable bandwidth 2D low-pass, high-pass and band-pass filters with improved circularity

Abstract

This paper discusses two-dimensional (2D) finite impulse response (FIR) filter structures to achieve improved circularity and variability in bandwidth without restructuring. The P3 transformation employed in this work for the design of circular filters helps to achieve better circularity and less complexity. The variability is obtained by using two different approaches. In Method 1, the bandwidths of the 2D circular filters are changed by adjusting a parameter in the one-dimensional (1D) domain. In contrast to Method-1, Method-2 directly adjusts the bandwidths of the 2D filters using a parameter in the 2D domain. Low-pass, high-pass, and band-pass variable bandwidth filters are designed using both methods to illustrate the benefits of the two approaches. Comparing their implementation complexity, contour approximation error, and normalized root mean square error to those of other multiplier-less transformations demonstrates their efficacy. It can be seen that Method 1 and 2 respectively achieve around 5% and 20% reduction in the number of multipliers with a maximum normalized root mean square errors of 0.3129 and 0.3532 when compared to that of the 2D filters designed using the latest existing transformation.