Trim-to-Coherence Fourier Transform

We introduce a discrete Fourier transform technique which extracts more spectral information from a given time series data set than conventional discrete Fourier transform (DFT). Valid information is obtained between the spectral bins of conventional DFT, scalloping error is greatly reduced, and amplitude and phase of Fourier components are more true to the process under study as with conventional DFT. We call the general idea Trim-to-Coherence Fourier Transform, and its particular embodiment ‘Phase-Rotation Fourier Transform’. Treatment of the raw data is minimally invasive; e.g. there is no zero padding.