I have some 9000 points that are plotted on a graph:
[Full resolution]
Actually, the plot is n
FFT isn't a bad idea, but it's probably overkill here. Running or moving averages give generally poor results and should be avoided for anything besides late homework (and white noise).
I'd use Savitzky-Golay filtering (in Matlab sgolayfilt(...)). This will give you the best results for what you are looking for - some local smoothing while maintaining the shape of the curve.
-Paul