INTRODUCTION TO SYNTHESIZERS - hol.gr

The illustration above shows a simple wave being sampled. The dotted lines show the sampling points. The
original waveform is the smooth line, and the sampled wave is the jagged line.
As we can see, the sampled version of the original wave suffers severely from the low sampling frequency. Since
the A/D-converter doesn't "know" what happens between to adjacent sample points, it will miss a substantial
amount of the wave. The result is a poor representation of the original wave, with a lot of jagged edges. These
edges will be heard as overtones not present in the original sound. This phenomena is called "aliasing".
Now let's see what happens if we double the sampling frequency!
The sampled curve is still a bit jagged, but is now much closer to the original waveform. As the sampling
frequency increases the sampled waveform is getting to look more and more like the original wave. It is fairly
obvious that a high sampling frequency is very important to achieve an authentic result.
But it shouldn't take long to figure out that a high sampling frequency will also consume available storage space
very quickly - there are simply more measurements to be stored in the memory.
Since the available memory usually is a very limited resource in a sampler, it's a tradeoff between sound quality
and sample length. Given a certain amount of memory, we can either achieve a longer sampling by lowering the
sampling frequency and thereby decreasing the sample quality, or we can achieve high quality reproduction by
sacrificing the length of the samples. It takes a lot of skill to learn how to balance these values for an optimum
performance!
Sampling resolution
A high sampling rate may still not be enough to make a good sample - we also need to have a high sample
resolution.
The resolution is the "exactness" of each individual sample. With a high resolution, each sample point will be
measured very accurately. With a lower resolution, the measurements will not be quite as exact, and a certain
amount of rounding errors will occur. Instead of getting too deeply involved with the technical aspects of this,
we can just say that a higher sampling resolution will yield a better reproduction of the original sound than a
lower resolution at the same sampling rate.
Sampling resolution is measured in the unit "bits". Usual sampling resolutions are 8-bit, 12-bit, 16-bit and 32
bit. A sampled sound with 8-bits resolution sounds very gritty and "coarse" compared with a 16-bit sample.
Almost all modern samplers are capable of 16-bit resolution sampling, or even 32-bit resolution sampling, which
yields a very high quality reproduction. In some samplers the resolution is a fixed property of the A/Dconverter,
but other samplers allow the user to set the resolution value to obtain a dirty, artificial and
"industrial" sound
Transposition
Once the waveform has been sampled and stored in memory, we need to be able to reverse the process to play
back the sample. This time the stored values are read out from the memory and the original waveform is thus
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