Date: Thu, 26 Feb 2015 22:04:39 +0000
From: Fons Adriaensen <fons(a)linuxaudio.org>
To: Cedric Roux <sed(a)free.fr>
On Wed, Feb 25, 2015 at 11:46:37PM +0100, Cedric Roux wrote:
can someone explain to me what this bandwidth
computation means?
There is nothing magical about it, it's just a pragmatic
approximation that results in the 3dB BW (for high + or -
gain) being expressed in octaves.
Expressing the BW in a logarithmic unit (such as octaves)
make sense because the magnitude response of a second order
parametric is symmetric on a log(f) scale but not on a linear
one.
An absolute value in Hz or even a relative one (the same divided
by center frequency) is informative only for small BW, where the
linear distance to the -3dB points left and right would be more
or less equal.
For large BW values (as often used in sound engineering) this
is no longer true. For example for a center frequency of 1 kHz
and two octaves BW the -3dB points are at 500 Hz and 2 kHz.
For four octaves that would be 250 Hz and 4 kHz, giving a -3dB
BW in Hz that is larger than twice the center frequency, which
is somewhat counter-intuitive.
The 'mathematical' way to define the BW of an second order
allpass would be at the +/- 90 degree phase points. This also
corresponds to the -3 dB points for an infinite notch, as used
by M & R. But keeping this value fixed in a parametric results
in curves that are not even symmetric for + and - gains. The
'bumps' would be much wider than the 'notches'. The sqrt (gain)
factor restores this symmetry. But using this means that there
is no longer any simple relation to what looks like bandwidth
on a frequency response plot and the actual 'mathematical'
value.
Ciao,
--
FA
A world of exhaustive, reliable metadata would be an utopia.
It's also a pipe-dream, founded on self-delusion, nerd hubris
and hysterically inflated market opportunities. (Cory Doctorow)
----- End forwarded message -----
--
FA
A world of exhaustive, reliable metadata would be an utopia.
It's also a pipe-dream, founded on self-delusion, nerd hubris
and hysterically inflated market opportunities. (Cory Doctorow)