if at the side of the graph, you plot the individual fourier transforms magnitude, with a slider bar to indicate magnitude of the deviation, and phase, to indicate how many days into the cycle we are today from its neutral point. and do this fourier transform for the 1 to 200 day exponential movinig averages, ie. EMA(40) would be fourier transformed independently from EMA(50) , and you did this say every 5 days at least, 1,5,10,15,20,25,...,200
this would be a very useful indicator for selling short and rebuying at a lower price if the cycles could be strongly established within reasonable time frames, you might even want to do it daily EMA(1),EMA(2),EMA(3),...,EMA(200) for completeness.