parabolderiv

Differentiates a vector of (sampled) data using the derivative of local parabolic fits to the data.

This program differentiates an empirical function (an array of evenly spaced values), for instance periodically sampled data from an experiment.

Method used: basically, a parabola is fit from k points to the left to k points to the right of the point where the derivative is required, this
is then analytically differentiated. These calculations are not actually performed, but the method as given by Lanczos in Ref. [1] is used: only 1 fit parameter of the parabola is needed, which is calculated directly from the data; at the edges a parabola is fit through the first (last) 2k points, from which the derivative is calculated directly. Additional information (on accuracy, &c.) in Ref. [2]. Noise is handled well. An
example from Ref. [1] is included.

The datapoints need to be equidistant. If the graphics_flag is set, the result of this method is compared to applying the standard MATLAB diff() function on the raw data as well as on adjacent averaged filtered data (zero phase delay). The example commands given illustrate this.

References:

[1] Applied analysis / by Cornelius Lanczos (3rd print., London:
Pitman, 1964 )

[2] Digital filters / by Richard W. Hamming (3rd ed., Englewoood Cliffs:
Prentice-Hall, 1989 )