Quote:
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**PelPix** I meant effect processing specifically.

Wouldn't a reverb applied to a 192kS/s waveform be more defined and regular across a given time period than one applied to a 44.1kS/s waveform because the reverb has more samples to process?

You raise a good point and one worth going into in greater detail. Hopefully when you've finished reading this post, digital audio will make a lot more sense.

When considering digital audio, there comes a point when our logic of what we see and know let's us down and we start to assume things about digital audio which are incorrect. This is because we are missing some vital information about how digital audio works and without this information the reality of how digital audio works appears counter-intuitive. I'll try to explain the missing information as simply as I can:

**Sampling Theory**
Imagine a perfect circle. If we wanted to store and recreate that circle perfectly on a computer, logic would indicate that the more points we measure and store round the circumference of the circle, the more accurately we can recreate it. Although, we would never be able to recreate the circle absolutely perfectly because the circumference of a circle is actually made up of an infinite number of points and we can't measure or store an infinite number of values. But there is a completely different approach to this problem. Let's say we only measure and store 3 points on the circumference of the circle. Let's also say that we give the computer some limitations; it's only allowed to draw perfect circles, for example. Now if we give the computer those three points we measured, the computer will be able to recreate our original circle absolutely perfectly. It doesn't matter that there are only 3 points, as any perfect circle which intersects those 3 points must be identical to the original. Measuring and storing 10 or 1,000 points is not going to make our recreated circle any more accurate than using just 3 points!

Although digital audio is a lot more complicated, the basic basic concept is the same as with this analogy of the circle above. As with the circle example, we have to place some limitations on the system for it to perfectly recreate sound waves: The system can only recreate sine waves and we must take more than two measuring (sampling) points per sine wave. As with the circle, providing we have more than two measurements (sampling points) the sine wave can be recreated perfectly. A million sampling points does not make the sine wave any more perfect (linear).

But, I here you say, sound waves are a lot more complex than simple sine waves. True, but that's missing a fundamental fact: Any sound you can hear is constructed from sine waves as the human ear can only respond to sine waves. So if we can perfectly capture sine waves, by definition we can perfectly capture all sound. The other limitation we mentioned above (more than two sampling points per sine wave) explains the Nyquist Point: That the sampling rate must be at least twice as fast as the highest audio frequency we wish to capture. So the Nyquist Point of 96k sampling rate is 48kHz.

Remember though, the practical application of sampling theory brings us into the world of electronic engineering and the trade-offs mentioned in my original post. However, digital audio is based on the concept of perfect linearity (unlike any other audio recording technology) and modern digital equipment can can get us surprisingly close to this ideal.

**Background**
In 1928 Harry Nyquist came up with this sampling theory. Nyquist was working for Bell Labs at the time and his sampling theory was designed for use with telecommunications signals. Nyquist's paper was nothing more than interesting research until twenty years later a genius mathematician (Claude Shannon), mathematically proved Nyquist's theory (turning it into a theorem) and incorporated it into his much grander Information Theory. Information Theory has a wide number of applications, from neurobiology to the understanding of Black Holes. Information Theory isn't just the basis digital audio but of all digital information. Claude Shannon is often referred to as the father of the digital age. However, it would be nearly another 20 years (1960's), until technology had advanced enough, to enable research to start into turning the Nyquist-Shannon Sampling Theorem into a practical digital audio system (by NHK, the BBC, et al.). The rest is history!

Summary
In my opinion, most of the audio industry exploits the fact that few consumers have an understanding of the Nyquist-Shannon Sampling Theorem to peddle their "bigger numbers is better" hype. The fact that a lot of audiophile magazines and reviewers also seem ignorant of the Theorem and it's implications also adds to the misinformation. If you take nothing else away from this post, just consider these 3 facts:

1. The Nyquist-Shannon Sampling Theorem provides for the capture and perfect recreation of

**all** the information contained in any sound we can hear.

2. The Nyquist-Shannon Sampling Theorem is mathematically proven and scientifically uncontested.

3. If the Nyquist-Shannon Sampling Theorem is incorrect, there would be no digital audio or indeed no digital age at all!

G

MIT paper:

Shannon Information TheoryEdited by gregorio - 9/12/11 at 4:57am