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