Recursive filters

Syntax: FILTER\RECURSIVE x f c d

If the \RECURSIVE qualifier is used, the third parameter, c, must be a vector, and the fourth parameter, d, must also be a vector. The data array, x, is processed through a recursive filter. This allows for the specification of a completely general recursive filter of arbitrary length. The values of c are the filter coefficients which operate on the data. The values of d are the filter coefficients which operate on the previously made output.

where is the length of vector c and is the length of vector d.

Integrating recursive filters

The trapezoidal rule integration filter:

The Leo Tick formula for integration:

See Table 7 for the trapezoidal rule and the Leo Tick formula integrating recursive filter coefficients.

Table 7:   Integrating recursive filters
type data coefficients output coefficients
Trapezoidal rule   [ 0.5; 0.5 ]  [ 1 ] 
Leo Tick formula   [ 0.3584; 1.2832; 0.3584 ]   [ 0; 1 ] 

  Nonrecursive filters
  Examples