filter Function

public pure function filter(b, a, x, delays) result(rst)

Applies the specified filter to a signal.

The description of the filter in the Z-transform domain is a rational transfer function of the form:

$Y(z) = \frac{b(1) + b(2) z^{-1} + ... + b(n_b + 1)z^{-n_b}} {1 + a(2) z^{-1} + ... + a(n_a + 1) z^{-n_a}} X(z)$, which handles both IIR and FIR filters. The above form assumes a normalization of a(1) = 1; however, the routine will appropriately handle the situation where a(1) is not set to one.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	b(:)	The numerator coefficients of the rational transfer function.
real(kind=real64),	intent(in)			::	a(:)	The denominator coefficients of the ration transfer function. In the case of an FIR filter, this parameter should be set to a one-element array with a value of one. Regardless, the value of a(1) must be non-zero.
real(kind=real64),	intent(in)			::	x(:)	An N-element array containing the signal to filter.
real(kind=real64),	intent(in),	optional,	target	::	delays(:)	An optional array of length MAX(size(a), size(b)) - 1 that provides the initial conditions for filter delays, and on ouput, the final conditions for filter delays.

Return Value real(kind=real64), allocatable, (:)

An N-element array containing the filtered signal.