LTPDA Toolbox™  contents 

Derivative estimation on discrete data series is implemented by the function ao/diff. This function embeds several algorithms for the calculation of zero, first and second order derivative. Where with zero order derivative we intend a particular category of data smoothers [1].
Method  Description 

'2POINT' 
Compute first derivative with two point equation according to: 
'3POINT' 
Compute first derivative with three point equation according to: 
'5POINT' 
Compute first derivative with five point equation according to: 
'FPS' 
Five Point Stencil is a generalized method to calculate zero, first and second order discrete derivative of a given time series. Derivative approximation, at a given time t = kT (k being an integer and T being the sampling time), is calculated by means of finite differences between the element at t with its four neighbors:
It can be demonstrated that the coefficients of the expansion can be
expressed as a function of one of them [1]. This allows the construction
of a family of discrete derivative estimators characterized by a
good low frequency accuracy and a smoothing behavior at high frequencies
(near the nyquist frequency).

Frequency response of first and second order estimators is reported in figures 1 and 2 respectively.
pl = plist(... 'method', '2POINT'); b = diff(a, pl); pl = plist(... 'method', 'ORDER2SMOOTH'); c = diff(a, pl); pl = plist(... 'method', '3POINT'); d = diff(a, pl); pl = plist(... 'method', '5POINT'); e = diff(a, pl); pl = plist(... 'method', 'FPS', ... 'ORDER', 'FIRST', ... 'COEFF', 1/5); f = diff(a, pl);
pl = plist(... 'method', 'FPS', ... 'ORDER', 'SECOND', ... 'COEFF', 2/7); b = diff(a, pl); pl = plist(... 'method', 'FPS', ... 'ORDER', 'SECOND', ... 'COEFF', 1/12); c = diff(a, pl); pl = plist(... 'method', 'FPS', ... 'ORDER', 'SECOND', ... 'COEFF', 1/4); d = diff(a, pl);
Figure 1: Frequency response of first derivative estimators.
Figure 2: Frequency response of second derivative estimators.
Applying digital filters to data  Spectral Estimation 
©LTP Team