A direct solution to the interpolative inverse non-uniform fast Fourier transform problem for spectral analyses of non-equidistant time-series data

Abstract

A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an improvement upon previously reported iterative methods for such problems, and is competitive in terms of time complexity with more recently proposed direct NFFT inversions when considering comparable matrix pre-computation steps. The software is highly portable, and available as a convenient Python package using standard libraries. Given its mathematical simplicity however, it can be easily implemented on any platform.