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The non-equidistant fast Fourier transform (NFFT) is an extension of thefamous fast Fourier transform (FFT), which can be applied to non-equidistantlysampled data in time/space or frequency domain. It is an approximativealgorithm that allows to control the approximation error in such a way thatmachine precision is reached while keeping the algorithmic complexity in thesame order as a regular FFT. The NFFT plays a major role in many signalprocessing applications and has been intensively studied from a theoretical andcomputational perspective. The fastest CPU implementations of the NFFT areimplemented in the low-level programming languages C and C++ and require acompromise between code generalizability, code readability, and codeefficiency. The programming language Julia promises new opportunities inoptimizing these three conflicting goals. In this work we show that Juliaindeed allows to develop an NFFT implementation, which is completely generic,dimension-agnostic and requires about 2-3 times less code than other famouslibraries while still being one of the fastest NFFT implementations developedto date.

NFFT.jl: Generic and Fast Julia Implementation of the Nonequidistant Fast Fourier Transform