I have a system that gives me a noisy data set similar to the one generated by this matlab/octave code. The y-axis represents the signal intensity and the x-axis represents spatial distance.
noise = randn(1,512);
points = gaussian(512,.01);
noisy = points + .02*(noise');
The actual signal will be asymmetric and not the result of a gaussian function(but close). I can't create the noise accurately by hand and the underlying signal algorithmically so image these two together.
The goal is to construct an interpolating curve, using bicubic splines, based on only one data set of this signal. The signal cannot be captured multiple times and averaged together to remove the noise. Since the signal is noisy, I can't simply pick points every N samples as the interpolation points so I need to do some signal conditioning first.
I will not be able to use an exact model of the underlying physical process but the sources of noise are known and I can make some assumptions regarding the maximum slope and SNR. The interpolation is used to correct for manufacturing limitations so the curve is intended to be smooth(exclusive of noise) but for cost reasons is not. Therefore we don't expect any large deviations from this example.
My initial approaches used an M-point moving average filter to smooth the signal, then used polyfit handle the ends of the signal. This worked but could potentially reduce the center peak, if M is large enough. I've also since learned smoothing signals before interpolation is generally discouraged.
What would be a better approach to achieve this?