SineFit.jl
This package provides functions for estimating and accurately fitting a sine function to a given signal.
This is basically an improvement in robustness to only using LsqFit: clever
initial parameter guessing helps the least-squares fit converge quickly and
accurately.
Why?
Fitting a periodic function using FFT only doesn't always produce the correct frequency, as a discrete Fourier transform has a discrete frequency resolution and thus doesn't produce the correct frequency for all input data sets.
Fitting a periodic function using LsqFit only doesn't always converge properly, as there is e.g. not a unique phase shift fit parameter.
Combining the two approaches, using an FFT to guess the initial fit parameters and then using a least-squares function fit, produces accurate results most of the time.