Smoothing

Median Filter

Median filtering involves taking the median of all values in a user-defined window for each value in a spectra. There are various methods of dealing with the ends of a dataset, which will naturally have a smaller window than the rest of the dataset. As an example, consider a "spectrum" with consecutive data points 13531.

Using a window size of three, and ignoring the endpoints for now: the median of 135 is 3. The median of 353 is 3. The median of 531 is 3. Thus, the three central points become 333.

There are various ways of dealing with the endpoints. One is to "extend" them out with the same values. Another is to decrease the window size of the median filter. Yet another is to not adjust them at all, leaving them the same.

Using the first method will give a spectrum of 13331. Using the second will give a spectrum of 23332. And using the third will give a spectrum of 13331 again. With such a small spectrum size, the differences are almost insignificant. However, for a more realistic spectrum they become more noticeable. None of these methods are inherently better than another; all have benefits and drawbacks. One should also remember that this only refers to the endpoints, not the center of a spectrum. Thus it's effect really isn't all that significant. Vespucci uses the first/second/third method.

Savitzky-Golay

Linear Moving Average

Truncated SVD Denoise

QUIC-SVD Denoise

Further Reading

An Overview of Median and Stack Filtering by Moncef Gabbouj, Edward J. Coyle, & Neal C. Gallagher Jr.