SavGol

Savitzky-Golay smoothing moves a small window along each row, fits a polynomial to the values inside the window, and uses the fitted polynomial to replace the centre value. This keeps broad peaks and trends while reducing short-scale noise. The same fit can also provide a derivative. Rows are samples and columns are channels.

The SavGol app lets users choose the window, polynomial, derivative, and edge settings, inspect individual samples, apply the calculation to all rows, and export the result.

Start

addpath('path/to/SavGol')
SavGol_test
app = SavGol(spectra);

The constructor accepts a numeric vector or matrix, or a struct with data/spectra and an optional wavelength/wavelengths/xAxis field. Rows are samples and columns are channels. A numeric vector becomes one row; matrices are not transposed.

Parameters

Parameter	Rule	Default
Window size	Odd integer, at least 3, no longer than the signal	11
Polynomial order	Integer from 0 through windowSize - 1	3
Derivative order	Integer from 0 through min(polyOrder, 3)	0
Edge method	extrapolation, reflection, replication, or none	extrapolation

The window uses natural window-size steps and adapts its limits to the loaded signal. The derivative order is limited to 3. The sample selector changes the displayed row only; Apply processes every row.

reflection mirrors samples without repeating the endpoint. replication repeats endpoint values. none uses zero extension. extrapolation extends a polynomial fitted at each edge.

For derivatives, the x-axis must increase or decrease at a constant spacing. Its signed spacing determines the derivative units and sign, including for a descending axis. Smoothing without derivatives does not need equal spacing.

Use the calculation without the window

addpath(fullfile('path/to/SavGol', 'business_logic'))
filter = SavGolFilter();

% First derivative with 0.25 x-units between channels:
dy = filter.filter(y, 11, 3, 1, 'extrapolation', 0.25);

The result keeps the row or column shape of the input. The second output is the convolution kernel used by the fit.

Result

After Apply, app.getData() returns:

• data and spectra: filtered samples-by-channels matrix
• wavelength and wavelengths: x-axis values
• metadata: method, window, polynomial order, derivative order, edge method, spacing, and application time
• isCurrent: false after parameters or input data change

Export uses the same data and x-axis values. Preview sampling does not change the full result.

Example data and checks

SavGol_test.m creates spectra and wavelength with different noise levels:

SavGol_test
app = SavGol(spectra);

Run Code Analyzer from this folder:

checkcode('SavGol.m', '-id')
checkcode('business_logic/@SavGolFilter/SavGolFilter.m', '-id')
checkcode('business_logic/@DataValidator/DataValidator.m', '-id')

MATLAB R2022a or later is required. No additional toolbox is needed.

Reference

Savitzky, A. and Golay, M. J. E. (1964). Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36(8), 1627-1639.

License: MIT