SYNTHESIS AND POLYPHASE IMPLEMENTATION OF wide-band LOW-PASS CIRCULAR 2D FIR FILTERS

An analytical synthesis technique in the frequency domain is proposed for a particular class of 2D filters, namely circular wide-band low-pass FIR filters. The design starts from a low-pass prototype filter which is ideally maximally flat, with specified bandwidth, based on hyperbolic tangent function. This is approximated as a trigonometric polynomial using a change of variable and the Chebyshev series, thus obtaining the factored frequency response of the FIR filter prototype. Applying a specific frequency mapping derived from the more general McClellan transform, the frequency response of the desired circular 2D FIR filter results directly, also in factored form. The designed filter has an accurate shape, with negligible distortions. We also proposed a computationally efficient implementation at system level, based on polyphase decomposition and block filtering approach, which leads to a filtering structure with low aritmetic complexity and a high degree of parallelism.