Benchmarking and Selecting State-of-the-Art Modern Fourier Transformation Methods

Abstract

Fourier transforms remain critical to scientific simulation, signal analysis, and modern machine learning workloads, yet practical performance leadership is conditional on workload structure, precision policy, memory limits, and platform behavior. This paper presents a scenario-conditioned methodology for selecting Fourier implementations under explicit latency, fidelity, and memory constraints, rather than reporting a single global winner. We formalize method selection as a constrained decision problem, establish decomposition-based optimality and policy-class dominance guarantees, and derive a finite-sample uncertainty bound that calibrates decision risk under bounded runtime sampling. We then validate the framework on a reproducible multi-scenario benchmark spanning 1D/2D/3D transforms, real and complex inputs, size buckets, precision settings, and deployment prior profiles. Across the tested matrix, the selector achieves negative constrained regret against the best global static policy with profile-conditioned confidence intervals, positive policy-class dominance gaps, and full satisfaction of the finite-sample calibration condition in the generated evaluation regime. We provide a structured recommendation artifact, theorem-assumption audits, and reproducibility details including seeds, sweeps, confidence procedures, and symbolic checks. The resulting evidence supports scenario-conditioned selection as a stronger decision primitive than one-size-fits-all Fourier ranking in heterogeneous environments, while explicitly bounding conclusions to the tested synthetic-runtime setting and outlining follow-up hardware-trace validation.