Design of 2-D Wideband Circularly Symmetric FIR Filters by Multiplierless High-Order Transformation

摘要

In this paper, we modify the original McClellan transformation to a $k$th-order version, and on the basis of the $k$ th-order McClellan transformation, we propose two high-order transformations for designing circularly symmetric wideband two-dimensional (2-D) digital FIR filter. The circularity of the resulting 2-D filters designed by our transformations is comparable to those 2-D filters designed by the other methods; however, the existing methods for circularly symmetric design cannot obtain a 2-D filter by the application of a single transformation on the 1-D filter response. By using the proposed transformations, in a single transformation on the 1-D filter, we can easily obtain the circularly symmetric 2-D digital FIR filter over a wide range of cutoff frequencies. Besides, with our approach, neither optimization procedure nor any computation is needed to obtain the transformation. Furthermore, since the implementations of the transformations are all multiplierless, the resulting 2-D filter has the same number of multipliers with the 1-D prototype filter. In the narrowband case, the 2-D transition width is shown to be narrower by a factor of about $sqrt k$ (and $sqrt {k + 1 / 2}$) than the transition width of the 1-D prototype filter. This means that the filter length required in the prototype filter is shorter than that using the existing methods.