Savitzky-Golay Smoothing

Features:

S-G smooths noisy signal data using a least-squares digital polynomial filter. Optimizes and visualizes the performance of the S-G smoothing algorithm on an individual spectrum from the selected region of interest using Savitzky-Golay smoothing.

Steps:

1.       Load the file.

2.       Select Spectra Mathematics → Savitzky-Golay smoothing.

3.       Press Select 1st Spectrum and draw a region of interest. A spectrum corresponding to the region will appear in the SPECTRAL ANALYSIS panel.

4.       Press Generate. A pop-up dialogue window will ask for additional parameters, Polynomial Order and Frame Size.

Polynomial Order corresponds to the degree of the polynomial fitted to the points in the moving frame. The default value is 2. Polynomial Order value must be smaller than Frame Size if the frame size is a positive integer. The default value is 10.

Frame Size modifies the frame size for the smoothing function. If the Frame Size value is greater than 1, the rolling window is the size of the input number (i.e., 10) and independent of the number of bands/channels. Higher values smooth the signal more with an increase in computation time. If the Frame Size is less than 1, the window size is a fraction of the number of points in the total number of channels. For example, if the Frame Size value is 0.05, the window size is equal to 5% of the number of points in the total number of channels.

When the process is complete, the new spectrum will replace the original image. We suggest clearing the spectrum by pressing Clear ROI/Spectra before drawing a new area of interest.

(Optional) The optimized parameters can be applied to the Savitzky-Golay filter

Additional Information:

IDCube uses a modified version of the Savitzky-Golay algorithm. The original algorithm developed by Savitzky and Golay assumes the input vector corresponding to the band/channel dimension has uniformly spaced separation units, while the current algorithm also allows one that is not uniformly spaced.

When the input bands/channels vector is evenly spaced, the least-squares fitting is performed once so that the signal is filtered with the same coefficients, and the speed of the algorithm increases considerably.

The algorithm specifies the degree of the polynomial fitted to the points in the moving frame. The default order of the polynomial fitted to the points in the moving frame is equal to 2. The default frame size is 10 samples. Both parameters can be modified in the IDCube.