приветы !

Прочитал на днях статью уважаемого человека - Dan Lavry, из Lavry Engineering. Lavry - строго для профессионалов. Статья о теории сэмплирования, конкретно о его частоте. Главный тезис -Засэмплированная волна содержит ВСЮ информацию без искажений, когда частота сэмплирования ВДВОЕ превышает самую высокую частоту сэмлируемого сигнала.

Это ОЧЕНЬ убедительно на мой взгляд.

Привожу вступление ( англ. )

Sampling Theory For Digital Audio By Dan Lavry, Lavry Engineering, Inc. Credit: Dr. Nyquist discovered the sampling theorem, one of technology’s fundamental building blocks. Dr. Nyquist received a PhD in Physics from Yale University. He discovered his sampling theory while working for Bell Labs, and was highly respected by Claude Shannon, the father of information theory.
Nyquist Sampling Theory: A sampled waveforms contains ALL the information without any distortions, when the sampling rate exceeds twice the highest frequency contained by the sampled waveform.
Introduction While this article offers a general explanation of sampling, the author's motivation is to help dispel the wide spread misconceptions regarding sampling of audio at a rate of 192KHz. This misconception, propagated by industry salesmen, is built on false premises, contrary to the fundamental theories that made digital communication and processing possible. The notion that more is better may appeal to one's common sense. Presented with analogies such as more pixels for better video, or faster clock to speed computers, one may be misled to believe that faster sampling will yield better resolution and detail. The analogies are wrong. The great value offered by Nyquist's theorem is the realization that we have ALL the information with 100% of the detail, and no distortions, without the burden of "extra fast" sampling. Nyquist pointed out that the sampling rate needs only to exceed twice the signal bandwidth. What is the audio bandwidth? Research shows that musical instruments may produce energy above 20 KHz, but there is little sound energy at above 40KHz. Most microphones do not pick up sound at much over 20KHz. Human hearing rarely exceeds 20KHz, and certainly does not reach 40KHz. The above suggests that 88.2 or 96KHz would be overkill. In fact all the objections regarding audio sampling at 44.1KHz, (including the arguments relating to pre ringing of an FIR filter) are long gone by increasing sampling to about 60KHz. Sampling at 192KHz produces larger files requiring more storage space and slowing down the transmission. Sampling at 192KHz produces a huge burden on the computational processing speed requirements. There is also a tradeoff between speed and accuracy. Conversion at 100MHz yield around 8 bits, conversion at 1MHz may yield near 16 bits and as we approach 50-60Hz we get near 24 bits. Speed related inaccuracies are due to real circuit considerations, such as charging capacitors, amplifier settling and more. Slowing down improves accuracy. So if going as fast as say 88.2 or 96KHz is already faster than the optimal rate, how can we explain the need for 192KHz sampling? Some tried to present it as a benefit due to narrower impulse response: implying either "better ability to locate a sonic impulse in space" or "a more analog like behavior". Such claims show a complete lack of understanding of signal theory fundamentals. We talk about bandwidth when addressing frequency content. We talk about impulse response when dealing with the time domain. Yet they are one of the same. An argument in favor of microsecond impulse is an argument for a Mega Hertz audio system. There is no need for such a system. The most exceptional human ear is far from being able to respond to frequencies above 40K. That is the reason musical instruments, microphones and speakers are design to accommodate realistic audio bandwidth, not Mega Hertz bandwidth. Audio sample rate is the rate of the audio data. Such data may be generated by an AD converter, received and played by a DA converter, or even altered by a Sample Rate converter. Much confusion regarding sample rates stems from the fact that some localized processes happen at much faster rates than the data rate. For example, most front ends of modern AD (the modulator section) work at rates between 64 and 512 faster than a basic 44.1 or 48KHz system. This is 16 to 128 times faster than 192KHz. Such speedy operation yields only a few bits. Following such high speed low bits intermediary outcome is a process called decimation, slowing down the speed for more bits. There is a tradeoff between speed and accuracy. The localized converter circuit (few bits at MHz speeds) is followed by a decimation circuit, yielding the required bits at the final sample rate. Both the overall system data rate and the increased processing rate at specific locations (an intermediary step towards the final rate) are often referred to as “sample rate”. The reader is encouraged to make a distinction between the audio sample rate (which is the rate of audio data) and other sample rates (such as the sample rate of an AD converter input stage or an over sampling DA’s output stage).

Далее идут схемы и рисунки с пояснениями. )))))