Savitzky-Golay Smoothing Filter

The Savitzky-Golay Smoothing Filter procedure in the Time menu or the Time toolbar offers effective time-domain smoothing for data sets with uniform X-spacing. The algorithm offers adjustable order, automatic sequential passes, and optional first through fourth smoothed derivatives.

The raw and smoothed data are shown in an AutoSignal Graph for rapid determination of the effectiveness of smoothing.

Time-domain smoothing can alter the frequency domain spectrum. If attenuation or artifacts within the frequency domain would be a problem, you should use one of the Fourier Smoothing and Denoising, Eigendecomposition Smoothing and Denoising, Wavelet Smoothing and Denoising options in the Process menu.

Savitzky-Golay

This time-domain method of smoothing is based on least squares polynomial fitting across a moving window within the data. The method was originally designed to preserve the higher moments within time-domain spectral peak data. The AutoSignal implementation of the Savitzky-Golay algorithm offers sequential internal smoothing passes to improve overall noise reduction.

To generate a fourth derivative, a minimum quartic (order 4) smoothing must be used. For a third derivative, a minimum cubic (order 3) smoothing is needed. Similarly, a second derivative requires a minimum quadratic (order 2) smoothing.

A higher order polynomial makes it possible to achieve a high level of smoothing without attenuating the extrema in the data. Because this algorithm relies on the linearity of an unweighted polynomial model, it is also quite efficient with large data sets.

The Savitzky-Golay procedure requires a constant X-spacing within the data. If needed, the Spline Estimation or Non-Parametric Estimation procedures can be used to generate uniformly spaced data.

Options

The Win n field specifies the one-sided width of the moving window. The smoothness will increase as the size of the window becomes greater. The Order specifies the polynomial model order. A quadratic (order 2) is the minimum. Orders through 12 are supported. Typically, Savitzky-Golay smoothing uses a quartic (order 4) polynomial. The Passes field specifies the number of sequential applications of the smoothing filter. In general, three passes is about optimum.

Process

The Savitzky-Golay procedure can smooth to a derivative. You can choose to simply smooth the Data, or you can smooth to a derivative (1st Deriv, 2nd Deriv, 3rd Deriv, or 4th Deriv).

Estimated Noise Reduction

AutoSignal offers a robust noise estimation procedure that may be of some value for low-frequency signals. A cubic polynomial interpolation is made for each point using the two points to the left and the two to the right (excluding the current point). The difference between the interpolated and signal values is used to generate a measure of the white noise present in the signal. This assumes that the signal can be locally characterized by a smooth cubic interpolant. Also, the signal component(s) should exist only in the lower quarter of the Nyquist range. If a high frequency signal component is present, these estimates of noise will be invalid.

The Raw Data value reports the estimated white noise in the incoming data, the Smoothed value the estimated white noise for the smoothed signal. The percent is given as the amount of estimated noise remaining after smoothing.

List

The List Data option lists the index, x-values, and the smoothed data. The listing uses the AutoSignal text viewer facility.

Copy

The Copy Data to Clipboard option copies the x values and smoothed data to the clipboard. Formats include full precision binary (for spreadsheets such as Excel) and ASCII (for pasting into text editors).

Save

The Save Data to Disk option writes the x-values and smoothed data to a supported file format. These formats include ASCII, Excel 97, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.

Production Facility

The AutoSignal Automation facility allows unattended processing of large numbers of data sets. The data sets can be consolidated in an Excel file or acquired using a DLL. The graphs can be exported to an MS Word RTF file, while the processed data can be exported to an Excel 95 or Excel 97 file.

If an Automation Session is in progress, the Reset button can be used to terminate the automated processing.

When exiting this procedure with the OK button, an option will be presented to update AutoSignal's main data table with the smoothed data.