5,586 research outputs found
Signal Flow Graph Approach to Efficient DST I-IV Algorithms
In this paper, fast and efficient discrete sine transformation (DST)
algorithms are presented based on the factorization of sparse, scaled
orthogonal, rotation, rotation-reflection, and butterfly matrices. These
algorithms are completely recursive and solely based on DST I-IV. The presented
algorithms have low arithmetic cost compared to the known fast DST algorithms.
Furthermore, the language of signal flow graph representation of digital
structures is used to describe these efficient and recursive DST algorithms
having points signal flow graph for DST-I and points signal flow
graphs for DST II-IV
The Falling Factorial Basis and Its Statistical Applications
We study a novel spline-like basis, which we name the "falling factorial
basis", bearing many similarities to the classic truncated power basis. The
advantage of the falling factorial basis is that it enables rapid, linear-time
computations in basis matrix multiplication and basis matrix inversion. The
falling factorial functions are not actually splines, but are close enough to
splines that they provably retain some of the favorable properties of the
latter functions. We examine their application in two problems: trend filtering
over arbitrary input points, and a higher-order variant of the two-sample
Kolmogorov-Smirnov test.Comment: Full version for the ICML paper with the same titl
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