RE: Nyquist Frequency (was Re: Looperlative LP1 - sample rate)

["Timothy Mungenast" <mungenast@earthlink.net>]

Excellent. I actually understood you and learned something!!
Cool.
~Tim


> [Original Message]
> From: jondrums <jondrums@hotmail.com>
> To: <Loopers-Delight@loopers-delight.com>
> Date: 12/15/2005 3:21:56 PM
> Subject: Nyquist Frequency (was Re: Looperlative LP1 - sample rate)
>
> >     Even though higher frequencies are indeed possible with a 192K 
> > sampling rate, it also means
> > that each waveform has more samples representing it, thus higher
fidelity. 
> > I never did understand
> > how the Nyquist theorum could claim fidelity in the upper end by only 
> > having two samples per
> > waveform.  Seems to me like you wouldn't be able to distinguish a
sawtooth 
> > from a sine from a
> > square wave if you only sampled at twice the highest frequency.
>
> Stephen -  It is my understanding that the Nyquist theorum actually 
> specifies the theoretical maximum frequency that can be represented with
a 
> digital signal.  It says nothing of the quality of that representation. 
> There's a key issue that makes the nyquist theorum all important to the
A/D 
> conversion process - frequencies higher than the Nyquist freq. will
manifest 
> themselves in the resultant digital signal as much lower frequency 
>noise. 
> That noise is basically garbage and is nearly unpredictable.
>
> Furthermore, frequencies that are close to but still less than the
Nyquist 
> frequency will be represented, however the amplitude of the
representation 
> will vary over time based on the _difference_ in frequencies.  How much
the 
> output varies in amplitude is a more complex equasion - important thing
is 
> that frequencies close to the Nyquist freq. (even though they are still
less 
> than) will be VERY distorted but will still be represented "perfectly 
> in-tune".  Example: 48KHz digital A/D converter could capture a 23KHz
pure 
> sine wave, and output a 23KHz sine wave whose amplitude varies at 1Khz -
you 
> would hear that 1Khz signal for sure!
>
> So this is a long story to explain the real meat of the issue - LOW PASS 
> FILTERING.  Any digital audio capture system must have low pass 
>filtering 
> before the A/D converter.  Ideally you would like to make sure that 
> absolutely no signals whose frequency is greater than the Nyquist
frequency 
> can be input to the A/D converter - because those will just cause 
>useless 
> garbage noise out the other end.  You also want to roll off frequencies
that 
> are close to the Nyquist frequency, because though could create ugly
garbage 
> noise too even though they will be represented somewhat.  These filters
are 
> called anti-aliasing filters and every digital audio system has them.
>
> The thing about filters is that even the most expensive filters don't 
>cut 
> off sharply at a certain frequency - instead they "roll off" slowly
starting 
> at 0Hz and gradually roll off more and more as the frequency goes up. 
> People refer to the "cut-off" frequency of a filter, but be aware that
this 
> is just the frequency at which the sound is sufficiently attenuated so
that 
> its much quiter than the original signal.   This means that a simple
filter 
> with cutoff frequency of 20KHz still passes 22KHz signals they're just
real 
> quiet.  It also means that this filter is rolling off your 18KHz signals 
> too.   The more money a manufacturer spend on the filter design and 
> implimentation, the "steeper" it is, but none can be infinately steep.
>
> So you've got to set your anti-aliasing filter well below the nyquist 
> frequency to be sure that nothing above the nyquist freq. of significant 
> volume can get through to the A/D converter.  If you don't have a lot of 
> money to spend on anti-aliasing filters (and most music equipment falls
into 
> this catagory) you use an off-the-shelf filter solution which doesn't
have 
> very steep filtering (and therefore has a cutoff freq. well below the 
> nyquist freq.).  This cheap filter will roll off frequencies well below
the 
> cutoff freq. too.    This could be what most people are hearing when 
>they 
> say 44.1KHz digital doesn't sound good.
>
> Ok, tired yet???   Well how about this one here - Time to learn about 
> anti-imaging filters.  This is just about the same thing as an
anti-aliasing 
> filter, but its on the other side of things - the outputs.   Every 
>device 
> that uses digital audio has to have one.   Typically it will be a similar
or 
> identical low pass filter to the anti-aliasing filter on the input.  
>This 
> further "rolls-off" some of the high end of your signal (even stuff 
>below 
> the Nyquist freq. - same as above).
>
> As a side note - the anti-imaging filter is the reason why you can buy a 
> really high end CD player and it can actually sound much better than a 
> crappy one even though both are using the exact same digital content. 
> (There are other reasons like upsampling though too) Same with sound
cards, 
> mixing desks, ect.   That's why a lot of people use SPDIF and do the
final 
> conversion only once on a high quality audio system.
>
> All of these things lead me to believe that even the most high quality 
> digital audio system can only do a very good job of representing
frequencies 
> less than about 1/3 of the sampling frequency.  This means that I
consider 
> 44.1KHz digital audio systems can represent up to 14.7KHz very well. 
That's 
> probably fine for most of the public, but there are many people who can
hear 
> this.   I believe that 48KHz is a pretty significant improvement with 
>the 
> ability to represent frequencies up to 16KHz quite well.   This is
probably 
> right around the actual threshold of most human beings and above this
starts 
> to become somewhat esoteric and specialized.  (keep in mind though that
DVD 
> supports 192KHz - so its not THAT esoteric -smile-).
>
> Jon
>
> If you got this far you don't need this link, but here is a decent 
> explaination of some of this with diagrams:
> http://www.cems.uwe.ac.uk/~lrlang/multimedia/audio2.pdf
> upsampling on high end cd players:
> http://www.mlssa.com/pdf/Upsampling-theory-rev-2.pdf
>