Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void SavGolayImpulse(TMtx *H, TMtx *Diff, int FrameSize, int Order, TVec *Weights = null); | Design a Savitzky-Golay polynomial smoothing filter. |
| 2 | void SavGolayImpulse(TVec *H, int FrameSize, int Order, TVec *Weights = null); | 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, int FrameSize, int Order, TVec *Weights = null);
Design a Savitzky-Golay polynomial smoothing filter.
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 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.
#include "MtxExpr.h"
#include "Units.SignalUtils.h"
using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Signal;
using namespace Dew::Signal::Units::SignalUtils;
void Example()
{
Matrix H, D;
Vector Data, Data1;
int Frs, Ord;
Data.Size(100);
Data.RandGauss();
Data1.Copy(Data);
Frs = 10;
if (!Odd(Frs)) Frs++;
Ord = 5;
SavGolayImpulse(H, D, Frs, Ord, nullptr); //single block processing
SavGolayFilter(Data, H);
}Overload 2: void SavGolayImpulse(TVec *H, int FrameSize, int Order, TVec *Weights = null);
The resulting H vector contains FIR type impulse response, which can be passed to the FirInit routine.
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.
#include "MtxExpr.h"
#include "Units.MtxExpr.h"
#include "Units.SignalUtils.h"
using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Math::Units::MtxExpr;
using namespace Dew::Signal;
using namespace Dew::Signal::Units::SignalUtils;
void Example()
{
Vector h(0);
Vector b = Ramp(300, TMtxFloatPrecision::mvDouble, 0, 0.1);
Vector c(b.Length);
TFirState state;
int n = 10;
int i;
SavGolayImpulse(h, 15, 7, nullptr);
FirInit(h, state, 1, 0, 1, 0);
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);
FirFilter(b, c, state);
}
FirFree(state);
}