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From: newton2@ucbtopaz.CC.Berkeley.ARPA
Newsgroups: net.audio
Subject: Re: Re CDs and square waves
Message-ID: <502@ucbtopaz.CC.Berkeley.ARPA>
Date: Sat, 23-Jun-84 03:41:09 EDT
Article-I.D.: ucbtopaz.502
Posted: Sat Jun 23 03:41:09 1984
Date-Received: Sat, 23-Jun-84 23:44:03 EDT
References: <3979@mordor.UUCP>
Organization: Univ. of Calif., Berkeley CA USA
Lines: 41

Here's another contribution to the discussion of square-wave response that
seems evergreen among audiophiles. 

First, in comparing the perceived sound from reproducing 20 kHz sine and
square waves, it seems to me that equal rms amplitudes is precisely what
you *don't* want- you want the audible components equal (a little question-
begging here, I'm afraid). If the rms values are equal, then 10% or so of
the energy of the square wave is in higher harmonics, versus 100% of the
sine wave concentrated at 20 kHz. You're trying to demonstrate that the
so-called ultrasonic components are audible, so shouldn't they be present
*in addition* to the 20 kHz component?

Second, as someone earlier pointed out, for a symmetrical waveform, the
first higher harmonic present is at 60 kHz, not 40 kHz. We're talking
BATS here, forget about Fido. Only tiny flying rodents (and golden-eared
audiophiles unconstrained by double-blind experiments) can hear this
stuff; only hunter-killer submarines and Polaroid cameras can emit it.

The Nyquist argument seems definitive to me-- the whole point of the anti-
imaging or reconstruction filter is to eliminate the ambiguity inherent
in the sampled data. Just asserting that alternating maxes and mins are
written "by a computer" on the disk doesn't show that a "square" was
written-- *every* sinusoidal component of the audio spectrum recorded 
on a CD could be interpreted as a poorly-reproduced squarewave, and
images-without-end (within the slewrate limit of the DAC) would be
reproduced absent the smoothing filter.

Speaking as an erstwhile audio designer (and only for myself), I find
squarewave testing the world's most wonderful shortcut in *quickly*
assessing what's going on phase/amplitude wise *in those well-behaved
circuits where it's useful*. Examples of such are DC-coupled amplifiers
and such, equalizers that are alleged to have "flat" positions and so
on. Examples of circuits that everyone either puts up with, assumes
are "perfect" or simple doesn't realize are ubiquitous are transformer-
coupled mic preamps, transformer-output mics, virtually all FM exciters,
"classic" tube amps, crossover networks (active or passive) and so on--
square wave testing is often uninformative for these circuits, which
nevertheless seem to perform sufficiently transparently (when well-designed)
to allow golden-earniks to hear right through to the special beeswax
Georg Neumann used to coat the capacitors in those priceless prewar tube
mics...:-)