An ultra-precise fast fourier transform – part 2

An earlier paper [1] describes the application of Prism Signal Processing to the Fast Fourier Transform (FFT), which generates high precision estimates of the frequency, amplitude and phase of spectral peaks. The current paper describes improvements to the Prism FFT. These include: a simplified calculation; applicability to shorter FFT window lengths (e.g. 1024 samples); improved performance against the Cramer Rao Lower Bound (CRLB), typically delivering root mean square errors of 2.2σ for frequency and 1.5σ, for amplitude and phase, where σ is defined as the square root of the corresponding CRLB. The method also delivers significantly reduced spectral leakage. MATLAB code implementing the Prism FFT is provided as an appendix.