# [LAD] [maybe OT] question regarding the FIL equalizer

Cedric Roux sed at free.fr
Wed Feb 25 22:46:37 UTC 2015

```Hi LAD,

I have a technical question regarding the FIL equalizer

The code uses Mitra-Regalia lattice filter (as described
in ). After reordering things here and there I see it's
indeed the case (surprise!).

 might be hard to get, but there is  with a lot of
details too, especially for bandwidth.

The only remaining point that I don't get is the bandwidth
manipulations.  uses for its parameter 'a' ('_s2' in FIL)
the formula:
a = (1 - tan(Omega/2)) / (1 + tan(Omega/2))
'Omega' being I don't really know what (-3dB notch bandwidth
for a gain of 0 maybe, if I read the paper correctly).

FIL uses bandwith expressed in octave and does:
_s2 = (1-b)/(1+b)
with:
b = bandwidth * 7 * (f0/fs) / sqrt(gain)
('f0' is the center frequency of the equalizer, 'fs'
is the sampling rate)

Reading  we see the factor 'sqrt(gain)' ('gain' is 'K')
that we find in the FIL's formula (specifically the formula
for k2 at page 13, after equation (17)).

But the "bandwidth * 7 * (f0/fs)" remains a total mistery
to me. It seems to be 'gamma' as found in , but 'gamma'
is way more complicated than what we see in FIL's code.

So the questions are:
- can someone explain to me what this bandwidth computation means?
- how it is derived starting from a bandwidth expressed in octave?
- And if we use the notations of  and  how do we relate it
to Omega or the various versions found in ? (which one is it by
the way? I thought it was the "at the bandedge frequencies the gain
is 'gain/2 dB'" one but it's not the case) (I wrote a little program
to plot things and as far as my program is correct bandedge frequencies
don't have a gain of 'gain/2 dB')

Regards,
Cédric.

 P. A. Regalia and S. K. Mitra, “Tunable Digital Frequency Response
Equalization Filters,” IEEE Trans. Acoust., Speech, Signal Process.,
vol. ASSP-35 (1987 Jan.).
 http://www.musicdsp.org/files/EQ-Coefficients.pdf
```