In this note we establish the mathematical framework for the filtering problem on a bounded interval, and provide a motivation for the use of the `half-sinc' function as a boundary filter. A boundary filter is one which yields output valid at the start or end of the interval on which the input is available. Such filters have obvious relevance to the problem of initialization for NWP. We also discuss some fundamental difficulties encountered when filtering time-limited functions.
Reference: Hirlam Newsletter Number 35.