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 ] |