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In this paper we propose a design method for a class of 2D linear filters, namely directional zero-phase IIR filters. Such filters are useful in detecting lines with a given angular orientation in an image. The design is achieved in the frequency domain and starts from 1D digital filters with given specifications. A zero-phase 1D filter is derived, whose frequency response is real and approximates to a certain accuracy the magnitude of the initial 1D prototype, using a convenient change of variable and a Chebyshev- PadÃ© rational approximation. As prototype filters, we use elliptic and inverse Chebyshev filters, which are very efficient. Design examples are presented and some simulation results on image processing are finally shown.