Support
Looper's Delight
|
Support |
|
|
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 >