Quite accurately estimate the four wave parameters for a (co)sine wave, using some simple statistics and FFT.

sinfit.jl

using DataFrames
import FFTW
import Statistics

"""
  estimate_wave_params(df::DataFrame, xsym::Symbol, ysym::Symbol)

Use Fourier analysis and statistics to find the best monochromatic sine wave parameters for data.

`xsym` and `ysym` are the column symbols for the x and y columns within DataFrame `df`, respectively.

Returns array of [amplitude, circular frequency, phase shift (radians), vertical offset].


"""
function ewp(df::DF.DataFrame, xsym::Symbol, ysym::Symbol)
	ydata = df[!, ysym]
	xdata = df[!, xsym]
	sample_rate = 1 / Statistics.mean(xdata[2:end] - xdata[1:end-1])
	
	offset = Statistics.mean(ydata)
	ampl = Statistics.mean(Statistics.quantile(abs.(ydata .- offset), 99/100)) - offset
	fft = FFTW.rfft(ydata)
	fftfreq = FFTW.rfftfreq(length(ydata), sample_rate)
  
  	# Determine dominant frequency and calculate phase shift.
	maxfreqloc = argmax(abs.(fft))
	maxfreq = fftfreq[maxfreqloc]
	shift = mod(atan(imag(fft[maxfreqloc]), real(fft[maxfreqloc])) + pi/2, 2pi)
	freq = maxfreq * 2pi

	[ampl, freq, shift, offset]
end

Smaller wave fits perfectly -- bigger wave (green) is not a good sine so the fit is not that good.