Timothy Stockman wrote: > A true square wave cannot exist in the real world. All > real-world square waves must be bandwidth limited to exist.
That's what they said about the imaginary numbers we mathematicians invented. They claimed they were imaginary and useless. > If you have a 20 KHz > square wave that's bandwidtch limited to 1 MHz and pick a Nyquist > frequency of 22.05 KHz, you've picked too low a Nyquist limit to > accurately reproduce the waveform. But if you pick a Nyquist frequency > of above 1 MHz, the waveform can be reproduced exactly. Right. That's real likely. Round the numbers to make it easier to see. 20kHz square wave, sample at 40kHz. result is 1, -1, 1, -1, 1, -1, ... Feed it through a DAC and you get a 20kHz sine wave. Double the sample rate to 80kHz, and you get a result of 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, ... which when you push it through a DAC, you get, a 20kHz sine wave. You are correct that real square waves rarely exist, and never exist in music. I think focusing on square waves is simply a red herring. > Rather it should be centered about what should be the > bandwidth limit and how it should be enforced. How much do components > above 20 KHz matter to the average human? What are the tradeoffs > involved in filter slope as the Nyquist limit gets farther from what is > important to the average human? Average? we are audiophile, we are much better than average. Again, RedBook is an ancient design and subject to many limitations both of the technology at the time and the business needs of the customers (big record labels and hardware manufacturers). The filters are a good place to explore. As are the intermodulation distortions between signals above 20kHz that can have audible impact well below that. Much more important to listeners is that the music buying public does not care about quality, and don't care about even RedBook specs. There will be no mass market high fidelity music, at least for 20 or 30 years. I could see some niche audiophile labels putting care into recording and mastering and selling music. I expect it will be sold as 24/98 because there are zillions of recording studios and recording gear that can capture that today. That we could be just as happy with 21 bits at 55kHz is really irrelevant, its gonna be 16/44 or 24/96 _______________________________________________ audiophiles mailing list audiophiles@lists.slimdevices.com http://lists.slimdevices.com/lists/listinfo/audiophiles
