ALMOST FREE SAMPLES
I’m back again for a third installment, encouraged by positive comments from people who are enthused about digital audio and anxious to learn more.
Surprisingly, a lot of you have confessed that you still haven't heard true digital reproduction; I strongly encourage you to visit a good stereo shop and take a listen, because I think you'll like it. Meanwhile I hope these columns pique your curiosity, sustain your interest, and develop your understanding of digital audio.
Thus, I'm forging ahead with more theory and explanation; stick with it and soon you'll be a bonafide digital audio expert.
So far we've discussed numbers, information, civilization, reality, and motorcycles. Our next topic relates to all of these, as well as everything else in the universe. First, some observations: Digital information can exist only in pieces, as discrete values, as numbers.
And that is a vastly different approach than with analog, in which one continuous, infinitely indivisible value is recorded. At first glance, you might think you're getting less for your money with digital--a finite number of fixed values as opposed to an infinitely changing one. In actuality, digital is often the better deal because we can more precisely manipulate discrete values and thus get more and more accurate information from the recorded data. That, more or less, is why digital computers are taking over the world.
With analog recording, we merely rolled tape or cut a groove, but with digital we must choose numbers. The first question we are faced with is: How many numbers do we want? In other words, how often do we record a data point? That is, how fast do we sample? And the idea of sampling is bound with the idea that relates to everything in the universe-and that is time. It is important for us because what we are dealing with is time sampling. This is the essence of what makes digital tick.
Speaking of ticking, and time, let's try a clock analogy to illustrate how a digital music system might differ from an analog system. Time seems to flow continuously (more on that later), and the hands of an analog clock sweep across the circle of hours, covering each part of time. A digital readout clock also tells time but with a discretey valued display; in other words, it displays a sampled time. It's the same with music. Music varies continuously n time and may be recorded and reproduced either in continuous analog form or time-sampled digital form. Just as both clocks each tell the same time, both types of recordings each play the same music.
Intuitively, a nagging question presents itself at this point in time. If a digital system samples discretely, what happens in between samples? Haven't we lost the information going on between samples? The answer, intuitively surprising, is no; given correct conditions, no information is lost. The samples contain the same information as the conditioned, unsampled signal. To illustrate this, let's try another analogy.
Let's suppose we mount a movie camera on the handlebars of a motorcycle and go for a spin, up and downhill, over smooth pavement and some not so smooth, and then we head back and process the film. When we audition our piece of avant-garde cinema, we discover that the discrete frames of film successfully come together to reproduce our ride, uphill and down; it looks great. But when we come to some bumpy pavement, our picture is blurred, and we ascertain that the quick movements were too fast for each frame to capture the change. We draw the following conclusions: If we increased .the film speed, using more frames per second, we would be able to capture quicker changes. And if we complained to City Hall and had the bad pavement smoothed, then there would be no blur even at slower frame speeds, and our movie would perfectly reproduce our motorcycle ride (except our hair wouldn't be blowing in the wind). We settle on a compromise; we have the roads fixed so no one feels the bumps, and then we use a film speed adjusted for a clean picture.
Just as the discrete frames of a movie create moving pictures, the samples of a digital audio recording create time-varying music; there is little conceptual difference between the visual and aural systems. In a digital audio system, we must smooth out the bumps in the incoming signal; specifically, it is low-pass filtered at 20 kHz.
When this above-audibility filtering is accomplished, we can successfully sample the signal such that there is no loss of information between the sampled signal at the output and the smoothed signal at the input. It is not an approximation; it is exact. When the input is smoothed, we can compute all the intervening values without error and thus re-create the original waveform smoothed at the outer limit of audibility. And fortunately, the sampling rate required to achieve this is well within our technology. The Nyquist sampling theorem shows that we must sample at a rate twice the highest throughput frequency to achieve loss less reproduction. Thus, for an input signal extending from 0 Hz to 20 kHz, we must sample at twice the highest frequency, or 40 kHz. And that is essentially what manufacturers have adopted, with a guard-band to make life easier on their hardware engineers; they need a little leeway because the analog filters used cannot cut off as suddenly as the sampling theorem would like. Thus, a few thousand hertz are allowed for the filter to sufficiently attenuate the signal. An alternative approach to these so-called brick-wall filters is the oversampling technique, in which the sampling rate is effectively extended to permit less drastic filtering. Regardless of the hardware design, the Nyquist theorem must be observed, and sampling must occur at least at twice the highest signal frequency. Compact Disc players, for example, sample at 44.1 kHz. Thus, 44,100 times a second, a CD player outputs a value. With stereo, that's 88,200 times per second. And over the course of an hour, that's about 3.2 million samples. For a Compact Disc costing $15, this means you're paying about 0.00050 per sample-almost free. At any rate, the point is clear: A smoothed signal may be sampled, stored in discrete values, de-sampled, and reproduced without any loss.
Of course, this discussion doesn't close the book on sampling. Later, we will discuss exactly why we have to have a low-pass filter at the input of a digital music system (and at the output, too), what happens if we don't, and why some digital systems choose sampling methods which require rates in the megahertz range. And time sampling is only half the battle; a digital system must also be able to determine the actual numerical values it will use at sample time to represent the original waveform's amplitude; we'll byte into that question next month.
Oh, I almost forgot! I mentioned that time seems to be continuous. However, some physicists have recently suggested that, like energy and matter, time also might come in discrete packets. Just as this magazine consists of a finite number of atoms, ;he time it takes you to read the magazine might consist of a finite number of time particles called "Nows." Specifically, the indivisible period of time might be 1 x 10^-42 seconds (that's a 1 preceded by 41 zeros and a decimal point). The theory is that no time interval can be shorter than this, because the energy required to make the division would be so great that a black hole would be created and the event would be swallowed up. If any of you out there are experimenting in your basements with very fast sampling rates, please be careful.
Also see: Philips Oversampling System for Compact Disc Decoding (April 1984)
(adapted from Audio magazine, Jun. 1984; KEN POHLMANN )
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