This paper proposes an analytical design method for two-dimensional square-shaped IIR filters. The designed 2D filters are adjustable since their bandwidth and orientation are specified by parameters appearing explicitly in the filter matrices. The design relies on a zero-phase low-pass 1D prototype filter. To this filter a frequency transformation is next applied, which yields a 2D filter with the desired square shape in the frequency plane. The proposed method combines the analytical approach with numerical approximations. Since the prototype transfer function is factorized into partial functions, the 2D filter also will be described by a factorized transfer function, which is an advantage in implementation. 1. Introduction Various design methods for 2D filters, both FIR and IIR, have been proposed by many researchers [1]. A frequently used design technique is based on a specified 1D prototype filter, whose transfer function is transformed using various frequency mappings, in order to obtain a 2D filter with a desired frequency response. Some relevant papers approaching 2D filter design using spectral transformations are [2–6]. A class of tunable 2D digital filters is discussed in [7]. The stability problem for 2D filters and stabilization methods are treated in papers like [8–11]. Diamond filters have been used as antialiasing filters in the conversion between signals sampled on the rectangular sampling grid and the quincunx sampling grid. Different issues related to design methods for diamond filters were studied in [12–14]. In [15], another design method for diamond-shaped filters was derived, starting from discrete filter transfer functions; two types of filters were obtained, one with complex transfer function and another with zero-phase transfer function. The latter is particularly appropriate for image processing applications as the filters introduce no phase distortions. The technique developed in [15] uses the 2D filter specification in polar coordinates. In this paper an analytical design method is proposed for 2D adjustable zero-phase square-shaped filters, a larger class of filters which may be regarded as a generalization of the common diamond filter. Starting from a 1D prototype filter with factorized transfer function, the corresponding 2D filters are obtained by a particular 1D to 2D frequency mapping. The 2D filter will have a factorized transfer function, which is a useful feature in implementation. This work mainly focuses on presenting the proposed method and describes in detail the design steps. Several design examples are also
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