Additional tests for filters

[csteinmetz1]

In addition to including test for all of the ITU compliance material test signals, we should include tests for the filter class that checks the coefficients against known values.

[csteinmetz1]

To properly test that filter coefficients are generated correctly we need to check our results against know good values. Here are some sources for the included filter designs:

Filter	Source
K-weighting	See page 4-5
Dash et al.	See page 15
Fenton/Lee 1 and 2	See page 4

We are looking to match these given values out to n number of decimal places. Something like 7 decimal places (based on limit of 32 bit IEEE 754 float) will certainly be acceptable. If something smaller is needed that is acceptable.

ITU-R BS.1770-4 provides filter coefficients for 48 kHz:

HPF	Value
b0	1.0
b1	-2.0
b2	1.0
a0	1
a1	−1.99004745483398
a2	0.99007225036621

Shelf	Value
b0	1.53512485958697
b1	−2.69169618940638
b2	1.19839281085285
a0	1.0
a1	−1.69065929318241
a2	0.73248077421585

Dash et. al provides filter coefficients for 48 kHz:

HPF	Value
b0	0.97456340
b1	-1.94912680
b2	0.97456340
a0	1.0
a1	-1.94894143
a2	0.94931217

Dip	Value
b0	0.98745685
b1	-1.89627528
b2	0.92513441
a0	1.0
a1	-1.89627528
a2	0.91259126