Boosted Whittaker-Henderson Graduation of Order 1: A Graph Spectral Filter Using Discrete Cosine Transform (Contemporary Mathematics, 2025)
The Whittaker-Henderson (WH) graduation of order 1 is a smoothing/filtering method for equally spaced one-dimensional data. Inspired by Phillips and Shi, this paper introduces the boosted version of the WH graduation of order 1. We show that it is a graph spectral filter using the discrete cosine transform, and then provide a simple formula for the (i, j) entry of its smoother matrix. We also show that it is a linear smoother such that the filter weights sum to unity and the smoother matrix is bisymmetric, i.e., symmetric and centrosymmetric. GNU Octave user-defined functions based on the obtained results are also provided.
Keywords: Whittaker-Henderson graduation; boosted Hodrick-Prescott filter; graph Laplacian; graph spectral filter; discrete cosine transform