Memory Complexity and Precomputation in Modern FFT Architectures

Author(s)	Mr. Tajinder Singh
Country	India
Abstract	This review reconsiders how fast Fourier transform (FFT) algorithms ought to be evaluated when the target hardware is no longer dominated by the cost of a complex multiplier. The classical literature, surveyed canonically by Duhamel and Vetterli[1], framed progress in terms of arithmetic reduction: multiplication counts first, then additions. We argue that this metric has lost much of its diagnostic value for the algorithms that now drive non-uniform sampling, sparse spectral recovery, and three-dimensional grid convolution. The relevant cost has migrated into the memory footprint of precomputed window tables, into the structure of sparse selection matrices, and into the oversampled grids that absorb interpolation error. We synthesise results from non-equispaced FFT theory, sparse deterministic schemes, biomolecular grid integration, and interferometric visibility simulation to show that modern speed-ups tend to be paid for in storage depth and precomputation overhead rather than in butterfly arithmetic.
Keywords	Fast Fourier transform, memory complexity, precomputation overhead, arithmetic complexity, non-uniform FFT.
Field	Mathematics
Published In	Volume 7, Issue 6, November-December 2025
Published On	2025-12-05

About IJFMR Fees & Payment Current Issue Publication Archive	Submit Research Paper Track Submission Status Publication Guidelines Publication Ethics Peer Review & Plagiarism	Join as a Reviewer Editors & Reviewers Reviewer Referral Program Get Reviewer Membership Certi.	Website/Journal Policies Usage Policy Content Policies Privacy Policy

Contact Us		+91-9687-828-838	editor@ijfmr.com

International Journal For Multidisciplinary Research