Interpolation in the DST and DCT domains

This paper presents the interpolation properties of the discrete sine and cosine transforms. Interpolation is a two-step process of upsampling to put zeros between data samples followed by filtering to fill in those zeros with interpolated values. Upsampling is accomplished by manipulating transform coefficients and the filtering is done using the convolution-multiplication property of the DSTs and DCTs. When working in the transform domain, the filtering can be done explicitly or implicitly. The explicit filtering requires multiplication by the transform of the filter coefficients but permits control over the frequency characteristics of the filter. The implicit method saves computation because there is no additional multiplication, just the forward transform followed by the longer inverse. New rules for the DSTs and DCTs are presented and explained.