andy_c wrote: > There's a really interesting post on this subject in, of all places, > Audio Asylum. A pro DSP guy named Werner set up an experiment wherein > he made a minimum-phase low-pass filter (with no pre-ringing, but plenty > of post-ringing) with a cutoff frequency of about 20 kHz. He looks at > the impulse response of the filter. Then he places an FIR filter after > it, with a cutoff frequency just a tiny bit higher than the 20 kHz value > of the minimum-phase filter. Does it add pre-ringing to the result? > No. That's because the pre-ringing of FIR low-pass filters is due to > the presence of spectral content at the cutoff frequency of the FIR > filter. But that content, in this case, has been removed by the > minimum-phase IIR filter ahead of it, so there's no pre-ringing in the > combined response at all. '_Here's_the_link_' > (http://db.audioasylum.com/cgi/m.mpl?forum=digital&n=146584).
I didn't get what he was trying to get at with these plots until I read the letters section of the issue of Audio Critic (from 1991. The math goes back to 1915!) that one of Archimago's commenters links to: "The pre- and postringing of the ideal brick-wall filter does not in any way introduce precur*sors or postcursors (?) which were not al*ready present in the original bandlimited signal which is being reconstructed from its samples. To believe otherwise is a serious misunderstanding of the mathematics involved, and hence of the true outcome. This may seem counterintuitive, but it is correct. For example, if the input analog signal was bandlimited by a causal brick-wall filter approximation (e.g., a minimum-phase analog antialiasing filter), which thus had no pre- cursors in its impulse response, an ideal sin x/x reconstruction will not introduce any precursors ." http://www.biline.ca/audio_critic/mags/The_Audio_Critic_16_r.pdf Bottom of page 6, top of page 7 (PDF pages 8 & 9). ------------------------------------------------------------------------ Daverz's Profile: http://forums.slimdevices.com/member.php?userid=32335 View this thread: http://forums.slimdevices.com/showthread.php?t=108876 _______________________________________________ audiophiles mailing list [email protected] http://lists.slimdevices.com/mailman/listinfo/audiophiles
