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Graph."],"published-print":{"date-parts":[[2016,11,11]]},"abstract":"<jats:p>Filters with slowly decaying impulse responses have many uses in computer graphics. Recursive filters are often the fastest option for such cases. In this paper, we derive closed-form formulas for computing the exact initial feedbacks needed for recursive filtering infinite input extensions. We provide formulas for the constant-padding (e.g. clamp-to-edge), periodic (repeat) and even-periodic (mirror or reflect) extensions. These formulas were designed for easy integration into modern block-parallel recursive filtering algorithms. 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