Documentation

Make a filter from the direct form. The direct form can be written as

H(z)=\Sum_{k=0}^{nb}b_k z^{-k} / (1-\Sum_{k=1}^{na}a_k z^{-k})$$

Cascaded second order sections are formed by finding the roots
of the direct form. The specified coefficients are $b_0$, $b_1$,...,
$b_{nb}$ for the numerator and $a_1$, $a_2$,..., $a_{na}$ for the
denominator. The argument $nb$ specifies the number of b coeffcients
supplied to the function minus 1, whereas $na$ is exactly the number
of coeffcients since $a_0$ is always 1 and omitted from the list.

Avoid the direct form since even fairly simple filters will run into 
precision problems.

Throws a runtime_error or invalid_argument exception, if an illegale 
arguments are specified.

Returns:

IIRFilter

Parameters:

fs - Sampling frequency
nb - Number of coefficients in numerator
b - Array of b coefficents
na - Number of coeffcients in denominator
a - Array of denominator coeffcients exclusive a0