Boundary conditions for Young-van Vliet recursive filtering

Young and van Vliet have designed computationally efficient methods for approximating Gaussian-based convolutions by running a recursive infinite-impulse-response (IIR) filter forward over the input signal, then running a second IIR filter backward over the first filter's output. To transition between the two filters, they use a suboptimal heuristic that produces significant amplitude and phase distortion for all points within about three standard deviations of the right-hand boundary. In this correspondence, a simple linear transition rule that eliminates this distortion is derived.