Applying harmonic balance to almost-periodic circuits

A new Fourier transform algorithm for almost-periodic functions (the APFT) is developed. It is both efficient and accurate. Unlike previous attempts to solve this problem, the new algorithm does not constrain the input frequencies and uses the theoretical minimum number of time points. Also presented is a particularly simple derivation of harmonic Newton (the algorithm that results when Newton's method is applied to solve the harmonic balance equations) using the APFT; this derivation uses the same matrix representation used in the derivation of the APFT. Since the APFT includes the DFT (discrete Fourier transform) as a special case, all results are applicable to both the periodic and almost-periodic forms of harmonic Newton.