Hi, I have a problem that may have a neat solution but I'm not certain of the approach. I'd like to find the inflection points of a function which is the sum (superposition) of sinusoids (tidal data).Its formulated like this:
y = A1*sin(w1*t + p1) + A2*sin(w2*t + p2) + … + An*sin(wn*t + pn)
where A1..An is the component Amplitude; w1..wn is the component frequency; p1..pn is the component phase. And each of these is known.
I think you can find the inflection by finding where the second derivative of y is zero. ie
y'' = 0 = -A1*w1^2*sin(w1*t +p1)+ A1*cos(w1*t +p1) + ..
Is there a fast way to determine the values of t (within a range) for which y'' =0? The timeseries is long (around 1 million points) so recreating the entire timeseries is time consuming.
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