Trillium Lane Labs Plug-ins Guide
64
Understanding Digital Distortion
Clients in the music industry regularly demand
the loudest possible mixes. In the process of
achieving such a “hot mix,” unwanted distor-
tion can be introduced. Intersample peaks that
exceed 0 dB may play without distortion in a
studio environment, but when the same mix is
played through a consumer CD player, the digi-
tal to analog conversion and oversampling pro-
cess can reproduce a distorted mix.
Digital Audio Theory
A key observation in digital audio theory is that
the entire waveform is represented by the sam-
pling points, but a reconstruction process still
needs to occur in order to recreate the waveform
represented. One cannot simply “connect the
dots” between sample points (as shown in
Figure 2) and yield the original waveform.
A waveform can be represented in multiple ways
during the process of sampling, display and re-
construction. Figure 3 through Figure 6 show
how the same complex waveform in Figure 2
can be represented in the digital domain.
The process of recreating the original waveform
from the sampled waveform involves a filter
called a reconstruction filter. This filter removes
all content above the Nyquist frequency (half
the sample rate). The range below the Nyquist
frequency defines the “legal” range of allowed
frequencies as frequencies in this range can be
accurately reproduced. All frequencies above
the Nyquist frequency do not adhere to Nyquist
or Shannon’s theorems regarding allowable fre-
quencies, cannot be reproduced and are there-
fore considered “illegal” frequencies. Because of
mathematical realities observed by Fourier in
the 1800’s and subsequently by Shannon in
Figure 2. Sampling
Figure 3. A complex waveform
Figure 4. Waveform sampled
Figure 5. Waveform as represented in DAW
Figure 6. Waveform as reconstructed at the D/A