sgolaydiff

Arguments

X

It can be either a real vector or a general real array. If it is an array the derivation is applied along the first non singleton dimension.

order

a positive scalar with integer value, the order of derivation.

C

a real nf by k+1 array: the matrix of differentiation filters computed by the sgolay function.

k

a positive scalar with integer value: the fitting polynomial degree.

nf

a positive scalar with integer value: the filter length, must be odd and greater the k+1.

w

a real vector of length nf with positive entries: the weights. If omitted no weights are applied.

D

A vector with identical shape as X, the estimated derivative.

Description

This function computes numerical derivatives using the FIR Savitzky-Golay smoothing Filter. This is achieved by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares.

order must be less than k

The (nf−1)/2 first and last derivative values are estimated by adding to the input signal, in reverse order and vertically symmetrized, copies of the first (nf−1)/2 points at the beginning and copies of the last (nf−1)/2 points at the end .

Examples

//generate a noisy signal
dt=0.01;
t = (0:0.01:4*%pi)';
x = sin(t)+0.03*rand(t,"normal");

clf();
//first order derivative
subplot(211)
dx = sgolaydiff(x,1,3,61);
plot(t(2:$),diff(x)/dt,'g',t,cos(t),'b',t,dx/dt,'r');
legend(["diff","theoretical","sgolaydiff"]);
//second order derivative
subplot(212)
d2x = sgolaydiff(x,2,3,101);
plot(t,-sin(t),'b',t,d2x/(dt^2),'r');
legend(["theoretical","sgolaydiff"]);
title("Second order differentiation")

Bibliography

Abraham Savitzky et Marcel J. E. Golay, « Smoothing and Differentiation of Data by Simplified Least Squares Procedures », Analytical Chemistry, vol. 8, no 36,‎ 1964, p. 1627–1639 (DOI 10.1021/ac60214a047)

http://en.wikipedia.org/wiki/Savitzky-Golay_filter.

See Also

• sgolay — Savitzky-Golay Filter Design
• sgolayfilt — Filter signal using Savitzky-Golay Filter.
• diff — 差分および離散微分

History