In this paper, we propose an infinite impulse response (IIR) filtering with complex coefficients for Euclid distance based filtering, e.g. bilateral filtering. Recursive filtering of edge-preserving filtering is the most efficient filtering. Recursive bilateral filtering and domain transform filtering belong to this type. These filters measure the difference between pixel intensities by geodesic distance. Also, these filters do not have separability. The aspects make the filter sensitive to noises. Bilateral filtering does not have these issues, but it is time-consuming. In this paper, edge-preserving filtering with the complex exponential function is proposed. The resulting stack of these IIR filtering is merged to approximated edge-preserving in FIR filtering, which includes bilateral filtering. For bilateral filtering, a raised-cosine function is used for efficient approximation. The experimental results show that the proposed filter, named IIR bilateral filter, approximates well and the computational cost is low.