Savitzky-Golay Spline Estimation

·    iI

 The Savitzky-Golay Spline Estimation procedure combines combines the full capability of the Savitzky-Golay Smoothing option with a B-Spline Interpolant.

 Like the Savitzky-Golay Smoothing option, this procedure directly generates a filter for the various derivative orders. The Savitzky-Golay algorithm is generally the best way to produce accurate smooth derivatives.

 This procedure does not automatically generate the uniformly-spaced data required by the Savitzky-Golay algorithm. If needed, the Spline Estimation or Local Regression Spline Estimation option can be used to create an interpolated data set with constant X-spacing.

 Win n, Order, Passes and Zero Edges

 These Savitzky-Golay algorithm controls are discussed in the Savitzky-Golay Smoothing option

 Constrained Cubic Spline

 This is discussed in the Spline Estimation option. The constrained cubic spline interpolant, which has no adjustments, will exactly pass through the smoothed data but will not evidence the wilder oscillations common to splines. This algorithm was selected to further stabilize estimates of derivatives, particularly those beyond first order.

 Output

 The principal output will interpolate the results from the zero-order Savitzky-Golay filter or Function. When the first, second, third, or fourth derivative (1st Deriv, 2nd Deriv, 3rd Deriv, 4th Deriv) is selected, the constrained cubic spline interpolates the results from the specified derivative filter.

 Note that the derivatives are based on the Savitzky-Golay filter, not the interpolating spline as is the case in the Smoothed Data Spline Estimation procedure. In that instance, smoothness and continuity of the derivative depended on the order of the spline. In this option, all derivative estimations are continuous and smooth, regardless of the derivative order being estimated.

 For the output, the number of elements n are generated between x start and x end. Up to 65536 values can be generated. The starting and ending X values should be at or within the range of the input data. The default values will perform a 2x upsampling within the x range of the data.

 Estimated Noise Reduction

 TableCurve 2D 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 data values is used to generate a measure of the white noise present. This assumes that the data can be locally characterized by a smooth cubic interpolant.

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

 The r-squared correlation coefficient is also reported. An rē of 1 is a perfect correlation while a value of 0 means the smoothed and unsmoothed data are completely uncorrelated.

 List

  The List Data option lists the index, time, and output in a three column table. The listing uses the TableCurve 2D text viewer facility.

 Copy

  The Copy Data to Clipboard option copies the time and output values 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 time and output values to a supported file format. These formats include ASCII, Excel, SPSS, or Systat.

 Production Facility

The Automation facility allows unattended processing of large numbers of data sets. The data sets can come from a text/CSV file or an Excel workbook. The graphs and reports can be exported to an RTF file or streamed to Microsoft Word, while the processed data can be exported to an Excel (xlsx) workbook.

The Reset button restores the data to its state when first entering the procedure.

 Residuals

  The Residuals button is used to graphically display the difference between the original and smoothed data.

 Numeric Summary

  The Numeric Summary displays a basic summary of the analysis and a listing of the Savitzky-Golay filter coefficients. If a derivative is currently selected, both the zero order data and the specified derivative coefficients are listed.

 Evaluation

  The Evaluation option offers the means to more extensively evaluate the spline model. The evaluation can be be direct, or the computation can consist of first or second derivatives, roots, or integrated areas. This option can be used to generate a table or file of any size using a generated X grid or by importing X data from supported file formats.

 MS Word/RTF Export

  The MS Word/RTF File Export option is used to save the current graphs and reports to either a MS Word file or a portable RTF (Rich Text Format) file. The graphs are inserted into the file as Windows metafiles.

 Automatic Update

 The List, Residuals, Numeric Summary, and Evaluation windows are automatically updated when any change is made to the algorithm's settings.

 Updating the Data Table

  When exiting this procedure with the OK button, an option will be presented to update TableCurve 2D's main data table with the estimated data.

 If Background Thread Fitting is active, the fitting will be initiated as soon as the estimation is accepted and the data is rescanned.