In this paper, four frequency sampling ﬁlter system functions which are classiﬁed as Type 1-1, Type 1-2, Type 2-1 and Type 2-2, are developed. Each type of these frequency sampling ﬁlter interpolates a frequency response through a speciﬁc set of frequency samples and also uses these frequency samples as coefﬁcients in each of their implementations. Each of these system functions are further developed for 2D linear phase ﬁlters that have real impulse responses and for 2D linear phase ﬁlters that have real impulse responses and fourfold symmetry. The approximate conditions for which these frequency sampling ﬁlters can implement narrowband 2D linear phase ﬁlters and narrowband 2D linear phase ﬁlters with fourfold symmetry more efﬁciently than direct convolution ﬁlters are also derived
System functions for 2-D linear phase frequency sampling filters.
Journal of the Franklin Institute, 341(4),