| Danman wrote on Wed, 17 November 2004 02:49 |
I'm not assuming anything. My A/D (and I think many of them) only supports 44.1, 48, 88.2, and 96. 88.2 would be a good choice, it seems.
Dan
|
Defining the optimal, amounts to finding a compromise point between various considerations. In the case of sample rate for audio, the main consideration is the ear bandwidth. Personally, I do not believe that people hear much above 20KHz, but there are some claims (however fuzzy) that we can “feel” 26KHz or slightly higher. Of course testing such theories requires use of microphones and speakers with higher than normal bandwidth…
So the theoretical answer is 40KHz for the “pragmatic”, 60KHz for the “open minded”.
But a theoretical sample rate does not yield a practical solution, because it calls for theoretical “brick wall” filters – perfectly flat pass-band to say 20KHz, total rejection above 20KHz. Clearly we need to have some practical margin, for real world filters.
In the “good old days”, that filter “near brick wall” requirement was directed towards the analog anti aliasing filter. We currently use the concept of over sampling. The front end of AD’s is operating at higher rates, thus the requirement for the analog filter (for anti aliasing) is greatly relaxed. Over sampling, however, does not solve it all. The requirement has been shifted from the analog AD front end to the digital side at the back end – the decimator.
Assuming a FIR type filter (for linear phase), using a 44.1KHz sample rate places some constrain on the AD decimation filter, it does take some significant compute power to perform the final decimation stage. There we pass 20KHz but block everything above 22.05KHz. In fact, a pass band is defined as a -3dB point – we really have only half the power at 20KHz! Does it matter? It does for some young ears and for exceptional ears!
48KHz improves the above situation. Say we use the same decimation filter that we used for 44.1KHz. The -3dB point (half power point) is now moved up by about 1-2KHz, but more important is the fact that we have virtually no loss at 20KHz. We now have flat response to over 20KHz.
There is a potential improvement going to 48KHz, and indeed one could argue a need to go to slightly higher frequencies. There is too much to say here for a single post. I am not aware of any REAL issues calling for greater than about 60KHz sampling. This is not a precise figure, perhaps 55KHz-65KHz is tight enough.
But we do not have such rates. Much of the real world is still locked into 44.1KHz, and some to 48KHz. For those that wish for a “positive margin”, 88.2KHz and 96KHz do make sense, because they are X2 multiples of 44.1KHz and 48KHz. A X2 multiple offers some value. An 88.2KH can be converted down to 44.1KHz at relative ease. The same is true for 96Hz to 48KHz. Such sample rate conversion is much easier than say 60KHz to 44.1KHz, though it may become a non-issue as sample rate conversion keeps improving.
Much of the sonic improvement going up to higher rates is due to the compounded effect of all the gear in the chain. Say your mic has a half power point at 20KHz (bandwidth). What does it do at say 18KHz? (there is some loss there as well). Add a speaker with say 20KHz bandwidth. Now your 20KHz is much lower, and the 18KHz is more impacted. Add an AD operating at 44.1KHz to the chain… Pretty soon and it does not take a golden ear there to notice the impact on flatness response…
It may be good to increase the AD sampling rate to around 60KHz. Is it wise to go a bit over 60KHz, given that the standards are in fact 88.2 and 96KHz. Going faster presents some negatives. Faster means compromising the accuracy, increasing the amount of data and increasing the required processing power (DSP).
