**14.3****
****Savitzky-Golay Peak Finding** (.NET, C#, CSharp, VB, Visual Basic, F#)

Class **PeakFinderSavitzkyGolay**
uses smooth Savitzky-Golay derivatives to find peaks in data. A *peak* is defined as a smoothed derivative
zero crossing.

**PeakFinderSavitzkyGolay**
extends **PeakFinderBase**, the abstract
base class for all peak finding algorithms, and an enumerable collection
of all found peaks.

**Creating Savitzky-Golay Peak Finders**

A **PeakFinderSavitzkyGolay**
instance is constructed from a vector of data, a window width, and the
degree of polynomial used to fit the data. For instance, this code builds
a data set from a sinc() function, then
constructs a peak finder with a width of 6,
and 4th degree smoothing polynomial:

Code Example – C# peak finding

var x = new DoubleVector(5000, 0.01, 0.1); DoubleVector data = NMathFunctions.Sin(x) / x; PeakFinderSavitzkyGolay pf = new PeakFinderSavitzkyGolay(data, 6, 4);

Code Example – VB peak finding

Dim X As New DoubleVector(5000, 0.01, 0.1) Dim Data As DoubleVector = NMathFunctions.Sin(X) / X Dim PF As New PeakFinderSavitzkyGolay(Data, 6, 4)

The constructor parameters must satisfy the following rules:

● The window width must be less than the length of the data.

● The polynomial degree must be less than the window width.

Typically, the degree of the smoothing polynomial is between 3 and 5.

**Savitzky-Golay Peak Finder Results**

Once you've constructed a **PeakFinderSavitzkyGolay**
object, the LocatePeaks() method finds all
peak abscissae and their smoothed ordinates in current data set:

Code Example – C# peak finding

pf.LocatePeaks();

Code Example – VB peak finding

PF.LocatePeaks()

The provided indexer on **PeakFinderSavitzkyGolay**
gets each peak as an instance of struct **Extrema**.
Property NumberPeaks gets the total number
of peaks found. For example, this code dump all peaks to the console:

Code Example – C# peak finding

for (int i = 0; i < pf.NumberPeaks; i++) { Extrema peak = pf[i]; Console.WriteLine("Found peak at = ({0},{1})", peak.X, peak.Y); }

Code Example – VB peak finding

For I As Integer = 0 To PF.NumberPeaks - 1 Dim Peak As Extrema = PF(I) Console.WriteLine("Found peak at = ({0},{1})", Peak.X, Peak.Y) Next

**Advanced Savitzky-Golay Peak Finder
Properties**

Additional properties on **PeakFinderSavitzkyGolay**
control the set of peaks that are found by the LocatePeaks()
method:

● SlopeSelectivity gets and sets the slope selectivity. The selectivity of the peak finder can be reduced by increasing the SlopeSelectivity. If SlopeSelectivity is set to 0 (default), all found peaks are reported.

● AbscisaInterval gets and sets the abscissa interval for the data. This is used to scale the derivatives to the correct units. For proper scaling of the peak abscissa locations, set AbscissaInterval to the data sample interval.

● RootFindingTolerance gets and sets the error tolerance
for the underlying **RiddersRootFinder**.
The default is 0.00001.

For instance:

Code Example – C# peak finding

pf.AbscissaInterval = 0.1; pf.SlopeSelectivity = 0; pf.LocatePeaks();

Code Example – VB peak finding

PF.AbscissaInterval = 0.1 PF.SlopeSelectivity = 0 PF.LocatePeaks()