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Re: [ARSCLIST] Sampling Theory (was Fred Layn's post on the Studer list re: Quantegy)
At 07:56 PM 1/16/2005 +0100, Goran Finnberg wrote:
> if anyone wants to hear about it again,
> I'll re-create it.
Okay, here goes.
Suppose the subject "cannot hear" anything above 15 KHz. That means that
higher pure tones (sine waves) are not audible on standard tests or by her
own experience. Set up two oscillators, one fixed at 8 KHz sine wave, the
other adjustable for frequency and level but generating square waves. The
challenge: adjust frequency and amplitude until the two match. Nothing
about the test except frequency response of the amplifier and reproducer
(speaker[s] or headphones) must extend beyond 25 KHz.
Simply put, no adjustment will cause the two to match. The best fit will
still leave the 8 KHz square wave sounding 'sharper'. That despite the fact
that elementary Fourier analysis shows the first difference between the two
signals is at 24 KHz, which the subject "cannot hear".
Once the subject has mastered that issue, repeat with sine and triangle
waves. The difference is more subtle, but still in dozens of tests the a
amtch cannot be achieved. Most subtle, so occasionally it fails, is square
vs. triangle. In that, the primary difference is phase of the harmonics
relative to the fundamental.
Conclusion: the ear is not linear. It is sensitive to the effects of
amplitude and phase of frequencies well beyond that at which it can sense a
We did this experiment back when AES was working on the standards for
CD-DA. A friend who was a member (and who has since passed away) joined me
for the planning and testing, but it was to no avail. Of course, the
objective was to get the sample rate above 44.1 Ksps so that phase could be
retained where it mattered most. Even in my home audio system, which is
good but far from the sort to satisfy 'golden ears', the difference between
CD and direct-to-disc recording on the best material (e.g., from Sheffield)
is audible and is in line with the tests above. Piano sound, where up to
the 13th harmonic is important, is seriously affected and where one can
easily distinguish among fine instruments from the LP, the lines are
blurred by the effects of sampling on CD.