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We present a novel way of approximating FIR filters by IIR structures through generalizing the vector fitting (VF) algorithm, popularly used in continuous-time frequency-domain rational approximation, to its discrete-time counterpart called VFz. VFz progressively refines the filter poles for improved approximation. Linear equation and eigenvalue solves are used in each iteration, with real-arithmetic formulation to accommodate complex poles. Comparison against conventional algorithms confirms that VFz exhibits fast convergence and produces highly accurate IIR approximants.