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: 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)