SignalUtils.SavGolayImpulse Method

Overload List

#	Signature	Description
1	void SavGolayImpulse(TMtx H, TMtx Diff, Int32 FrameSize, Int32 Order, TVec Weights)	Design a Savitzky-Golay polynomial smoothing filter.
2	void SavGolayImpulse(TVec H, Int32 FrameSize, Int32 Order, TVec Weights)	The resulting H vector contains FIR type impulse response, which can be passed to the FirInit routine.

Overload 1: void SavGolayImpulse(TMtx H, TMtx Diff, Int32 FrameSize, Int32 Order, TVec Weights)

Design a Savitzky-Golay polynomial smoothing filter.

#	Name	Type	Description
1	H	TMtx	source TMtx
2	Diff	TMtx	source TMtx
3	FrameSize	Int32
4	Order	Int32
5	Weights	TVec	source TVec

Result: stored in self (calling object)

Remarks:

Compute a Savitzky-Golay polynomial smoothing filter: a polynomial of degree Order is least-squares fitted to each FrameSize-long window of the signal. H is sized FrameSize x FrameSize; row i holds the filter producing the fitted value at window position i. Only the center row of H is used for filtering the signal interior, the upper and lower rows of H are applied to the transition regions where the signal starts and stops (see Dew.Signal.Units.SignalUtils.SavGolayFilter). Diff is sized (Order+1) x FrameSize; row k recovers the coefficient of x^k of the fitted polynomial, with x counted in samples relative to the window center, so row 1 is the first-derivative filter.

Weights, when assigned, must hold FrameSize strictly positive values and the fit minimizes the weighted sum of squares; H is then not symmetric. An exception is raised if FrameSize is not odd, if Order is not in [0, FrameSize-1], or if Weights are present with wrong length, non-positive values or a precision different from H. The computation runs in the precision of H.

Overload 2: void SavGolayImpulse(TVec H, Int32 FrameSize, Int32 Order, TVec Weights)

The resulting H vector contains FIR type impulse response, which can be passed to the FirInit routine.

#	Name	Type	Description
1	H	TVec	source TVec
2	FrameSize	Int32
3	Order	Int32
4	Weights	TVec	source TVec

Result: stored in self (calling object)

Remarks:

Returns the center row of the Savitzky-Golay smoothing matrix: the FIR filter fitting a polynomial of degree Order to each FrameSize-long window and evaluating it at the window center. Optional Weights (FrameSize strictly positive values, same precision as H) select a weighted least-squares fit.

Examples

using Dew.Math;
using Dew.Math.Editors;
using Dew.Math.Units;
using Dew.Signal;
using Dew.Signal.Units;
using Dew.Math.Tee;
using Dew.Signal.Tee;

private void button1_Click(object sender, EventArgs e)
{
    Vector h = new Vector(0);
    Vector b = MtxExpr.Ramp(300, TMtxFloatPrecision.mvDouble, 0, 0.1);
    Vector c = new Vector(b.Length);
    TFirState state = new TFirState();
    int n = 10;
    int i;

    SignalUtils.SavGolayImpulse(h,15,7,null);
    SignalUtils.FirInit(h,ref state,1,0,1,0);
    try
    {
        c.Size(b);
        n = 10;
        int bLength = b.Length; //must be outside of the "for" to prevent reevaluation
        for (i = 0; i < (bLength/n); i++)
        {
            b.SetSubRange(i * n, n); //select only a small subvector of the vector
            c.SetSubRange(i * n, n);
            SignalUtils.FirFilter(b,c,ref state);
        }
        MtxVecTee.DrawIt(new TVec[2] { b, c }, new string[2] { "Filtered data", "Original data" }, "Savitzky Golay", false);
    }
    finally
    {
        SignalUtils.FirFree(ref state);
    }
}