Originally Posted by VirusKiller
Something bothered me with something John Atkinson said in his review, but it wasn't until a re-read of Peter Craven's paper that I realized what it was:

Originally Posted by John Atkinson
On the face of it, however, this improvement seems paradoxical: the preresponse comprises ringing at half the sample rate (called the Nyquist Frequency), which, even with CD, is above the limit of human hearing. But the preresponse does appear to have an audible effect, perhaps because the human ear/brain system acts as a wavefront detector rather than as a spectrum analyzer.
John is mistaken and hasn't understood the problem fully. He notes, correctly, that the ringing occurs at the Nyquist frequency or 22.05kHz or 24kHz, but he's failed to appreciate that the ringing introduced by a brick-wall filter occurs at all frequencies present in the input signal and that it is the amplitudes of all these frequencies which modulate at the Nyquist frequency. It's the linear phase nature of the brick-wall filter which results in all frequencies modulating at the same (Nyquist) frequency. Ringing is therefore quite audible to human hearing, because it occurs at all frequencies present in the source; there is no paradox as stated.

Edit: Here's a picture of the typical impulse response of a brick-wall filter which plots the response amplitude for all frequencies (y-axis) vs. time (x-axis):

[Linked Image from stereophile.com]

Note the pre-ringing and post-ringing either side of the main (peak) response. Although the response varies in amplitude, the frequency of the response is the Nyquist frequency throughout.

Not sure I agree with your criticism of JA's article. You are correct that the ringing occurs when any transient passes through the filter. However, it is not the fact that the filter is linear phase that has them ring at the Nyquist frequency. Any filter with a rolloff steeper than 6 dB per octave will ring -- at its cutoff frequency. The sharper the knee, the more it will ring.

A filter rings at the Nyquist frequency (which is simply half of the sampling frequency) of a digital audio record/playback system because the designers used filters that had a cutoff frequency of 22.05 kHz. This is true whether the filter is linear phase, minimum phase, or any phase.

Charles Hansen
Ayre Acoustics, Inc.