Reproducibility Standards for Wavelet Transform Algorithms
Carl Taswell · 1998
Specifications for reproducibility standards are developed for wavelet transform algorithms. Reproducibility of an algorithm is defined as the requirement that the specified algorithm yield the same transform coefficients for the same signal data regardless of implementation in any programming language or on any computing machine. The specification is built with three heirarchical stages consisting of 1) filter bank coefficients, 2) singlelevel convolutions, and 3) multi-level transforms. Each stage is specified with all the necessary choices, parameters, and operators required to insure reproducibility. Each stage can be further characterized by additional properties that provide relevant information. The specification has been designed to be a sufficiently general and flexible framework which encompasses many different convolution types addressing the issues of both the phase shift and the boundary treatment. New convolution phase shift variants are introduced. In particular, a peak near-aligned phase variant is demonstrated on test signals and applied to fast wavelet based matrix multiplication. Finally, in the context of computational science and engineering, the concept of scientific reproducibility of an algorithm is discussed and contrasted with two other concepts introduced as repetitive executability and input-output repeatability.