Polyphase Implementation for Gaussian 2D FIR Filters with Circular Symmetry

We propose an analytical design procedure for a Gaussian-shaped circular band-pass 2D FIR filter and also a novel, efficient implementation of the designed filter based on a polyphase decomposition approach. This 2D filter is designed in the frequency domain using a specific frequency mapping applied to a band-pass 1D prototype having a Gaussian shape and imposed specifications (peak frequency, bandwidth). Since we start from a 1D prototype with a factored transfer function, the frequency response of the designed 2D filter also results directly in a factored form. This is a major advantage in actual implementation, since in this case the filter can be synthesized in a cascade structure, and the overall filtering can be achieved sequentially. The proposed implementation is described in a simpler case, namely for a smaller size of the filter kernel and also of the input image. Using the polyphase and block filtering approach, a convenient implementation is obtained for the 2D FIR filter at system level, with a relatively low computational complexity, i.e. a minimum number of arithmetic operations.