Examination of direct form vs. WDF realization of a 2-D quadrantal fan filter in FPGA hardware

The wave digital filter approach, introduced in 1986 by G. Fettweis, is a very advantagous approach for realization of digital filters, especially in higher dimensional cases, like image- and video-processing applications. If properly followed, it guarantees a stable system realization and low sensitivity to quantization errors, which is crucial for implementations on fixed point hardware. While these properties were broadly examined and discussed for 1-D systems in the past, 2-D filters are frequently implemented as FIR structures or carefully optimized IIR filters, due to missing knowledge about the necessary overhead of the WDF structure as well as its advantages. That WDF are still a timely filter design approach, especially for 2-D filters is shown in the present paper by means of a quadrantal fan filter, as frequently used for velocity filtering. We examine two different realizations of the same transfer function, once realized as a WDF, and once in a usual direct form. We compare hardware effort of both filters, as well as the degradation of the transfer function under reducing wordlengths.