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In this paper, we propose a novel approach to implement a pulse rate multiplier based on the temporal self-imaging effect using, for the first time to our knowledge, a birefringent optical filter. The proposed filter, with periodic quadratic phase-only filtering induced through engineered polarization mode dispersion, contains N-stage hybrid birefringent crystals set between an input polarizer and an analyzer. Each stage is composed of an identical section and a variable section. An optimization algorithm is used to determine the opto-geometrical parameters of the filter. Preliminary results for 10-stage, 12-stage, 16-stage, and 20-stage birefringent filters show very high fidelity for multiplying a 10 GHz input pulse rate by factors of two, four, six, and eight, respectively, without distorting the individual pulse properties.