Re: Frequency/Sample rate

On Jul 6, 12:58 pm, steve <stephen.mar...@xxxxxxxxxx> wrote:
technically, any waveform requires at least two samples per wave.

No, "mathematically", to fully replicate a waveform requires
MORE than two samples of the highest component of
that wave.

at two samples, for example, you really cannot tell
whether the waveform is sine, square, sawtooth, or whatever
variant the harmonics may imbue to the waveform. Even
at four samples, the original waveform is only approximated.
(i.e. sine can look square or sawtooth depending upon
at what degrees of arc the sample is taken.)

More than two, that's all you neeed, for the highest
component of interest: end of discussion.

that said, few humans can detect the difference between
a sine, square, or sawtooth above 10k.

I would challenge you to find said few humans.

This claim is made over and over again and it's flawed
beyond utility.

The test is almost always made with a standard lab function
generator whose output waveforem are normalized to have
the same peak aimplitude regardless of the waveform., e.g.,
the sine wave is 1 V peak-to-peak and the square wave is
1 v peak-to-peak.

Set the frequency to 10 kHz, and it's actually pretty easy for
most people to tell the different between the switch set to
sine wave and the switch set to square wave, but they are
NOT hearing the difference between a 10 kHz sine and a
10 kHz square wave: They're hearing the difference between
a 10 kHz sine wave with a peak-peak amplitude of 1 volt
and a 10 kHz sine wave with a peak amplitude of about 1.28
volts. That 1.28 volt sine wave is the amplitude of the 10
kHz sine wave fundamental of your 1 volt peak square wave.

That difference, almost 2 dB, is actually quite EASY to hear.

Now, go find us these few humans that can hear the
difference between a 10 kHz 1 volt P-P sine wave and
a 10 kHz 0.786 volt P-P square wave, and now you
might have something. But since no one else has
survived the challenge, I'd not place any hard cash on
you being the first.

But there is a difference.

Not when the signal is PROPERLY band-limited to less
than 1/2 the same rate, there isn't, other than simple in-
band amplitude differences.

How we as humans interpret that difference
is not easily quantifiable--some may speak in terms of
clarity, crispness, 'air', 'musicality', or what have
you--not very useful terms to the engineer.

It's not very quantificable because those making the
claims have never quantified it.

As well, sampling at a fixed frequency any other
frequency pattern will result in sampling-induced
harmonics, non-musical, that are in fact lower
than the fundamental of the wave. the amplitude
of these harmonics reduces greatly with increased
number of samples per wave, so at under, say, 5K,
they are not noticable, when sampling at 44.1k.

Complete and utter nonsense. As long as the signal
is bandlimited to less than 1/2 the sample rate, no
such artifacts exist. Period. That means any,
repeat ANY waveform that is bandlimited to less
than 1/2 the sample rate will be captured with NO
additional artifacts.

finally, the lower the sampling frequency, the
increased number of artifacts created when resampling.

Not as long as it is greater than twice the abndwidth, it
won't.

So, if one recorded some cuts at 44.1 and others at
48k, the movement back and forth to digitally (or analog)
mix will have the effect of altering the higher-frequency
waveforms in progressive generations of resampling.

Not for ANY waveform band-limited to 20 kHz, it won't.

the bottom line is that sampling at 44.1k has
a noticable and significant impact on all waveforms
over 11k, and some modest impact over 5.5k.

Again, complete nonsense.

Impacts increase with successive generations
of resampling (any time bit rate changes, and
in particular, compression.
Measuring whether humans can detect such a
change is torturously difficult.

Actually, it's not.

prior to the 96 and 192 rates, i found that recording
and mixing all within 44.1 resulted in less resampling
bias and artifacts than switching between 48 and 44.1.

What on earth is "resampling bias?"

And if this ain't the case, why would the sampling rate be called
"frequency?"

because the frequency of a sine waveform involves a
continuous function that goes both positive and negative
during one complete 'wave'. There are generally two
zero crossings during a wave. Let's say, for a moment,
that I sampled the audio energy at each zero
crossing--exactly two samples per waveform, or at exactly
22.05 KHz.

If you do this, you have violated Nyquist/SHannon. You have
a broken, defective sampler.

Why then take something that's broken and try to make any
sense or draw any conclusion from the result: IT'S BROKEN!

Then, upon playback, i iterpolate a straight line between
the samples.

During playback, you NEVER "interpolate a straight line."

What waveform would result?

Why would anyone care what waveform results from
your broken sampler? IT'S BROKEN!

.

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