NEW APPROACHES TO DIGITAL SUBTRACTIVE SYNTHESIS
Antti Huovilainen and Vesa Vdlimdki
Helsinki University of Technology
Laboratory of Acoustics and Audio Signal Processing
P.O. Box 3000, FI-02015 TKK, Espoo, Finland
ABSTRACT
Computationally efficient oscillator and filtering
algorithms for digital subtractive synthesis are
discussed. The oscillators algorithms include the
recently proposed differentiated parabolic waveform
generator and its modification. The algorithm generates
a signal that sounds similar to the analog sawtooth
waveform, because it suppressed aliasing that occurs
due to sampling of a non-bandlimited waveform. A
modified version of the nonlinear digital Moog ladder
filter is introduced. The new structure reduces the
computational cost of the nonlinear digital Moog filter
by using a single nonlinearity in the feedback loop
instead of four nonlinear functions inside filter sections.
The new digital Moog filter structure also decouples the
cutoff and the resonance parameters and offers several
response types by selecting a weighted sum of different
output points.
1. INTRODUCTION
Digital subtractive synthesis, which is also called virtual
analog synthesis, refers to computational methods that
imitate the sound generation principles of analog
synthesizers of the 1960s and 1970s. The basic principle
in subtractive synthesis is first to generate a signal with
a rich spectral content, and then to filter that signal with
a time-varying resonant filter.
Virtual analog synthesis became a popular and
commercial term in about 1995, when Clavia introduced
the Nord Lead 1 synthesizer, which was marketed as an
analog-sounding digital synthesizer that uses no
samples. Instead, all sounds were generated by
simulating analog subtractive synthesis. Previously, the
Roland D-50 synthesizer of the late 1980s worked in a
similar way although it contained sampled sounds. An
early example of an attempt to design a digital
synthesizer that sounds analog was Synergy [4].
What makes digital subtractive synthesis more
demanding than is generally understood is that imitating
analog electronics with digital processing is not as easy
as it may seem. One problem is aliasing caused by
sampling of analog waveforms that have sharp edges.
The spectra of such waveforms continue infinitely high,
and the signals are thus not bandlimited. Another
difficulty is that analog filters do not obey simple linear
theory. With high signal levels they generate distortion.
This does not naturally occur in digital processing, but it
must be designed and implemented on purpose, see for
example, references [8] and [3].
9 Filter Out
Osc2
Figure 1. A typical block diagram of subtractive
synthesis as it was implemented in the Prophet 5
synthesizer in late 1970s.
In this paper, we discuss new versions of oscillator
and resonant filtering algorithms that can sound like old
analog synthesizers.
2. SUBTRACTIVE SYNTHESIS
The electronic music modules introduced by Robert A.
Moog in mid-1960s [6] are one of the most important
innovations in music technology. A few years later, his
company introduced products where the various
modules, such as oscillators, filters, and amplifiers,
were integrated into a single portable unit. Subtractive
synthesis was the main principle used in these
instruments. Minimoog was one of the most popular
analog synthesizers in 1970s.
The Prophet 5 synthesizer introduced by Sequential
Circuits in 1979 has microprocessor controlled
electronics, but it is still an analog synthesizer. Its block
diagram shown in Fig. 1 is today a classic example of
the subtractive synthesis principle. It includes two
oscillators, a resonant lowpass filter, and two envelope
generators (ADSR). There are a couple of alternative
waveforms available together with a noise source.
3. DIGITAL OSCILLATORS
The sharp edges of geometric waveforms, such as the
sawtooth or the square wave, cause aliasing, because
such signals are not bandlimited. Three different classes
of methods are known to avoid this problem:
1. Bandlimited methods that generate harmonics
only below the Nyquist limit, such as additive
synthesis and its variants, e.g., wavetable
synthesis and the discrete summation formulae;
2. Quasi-bandlimited methods in which aliasing is
low and its level can be adjusted by design to
save computational costs, such as in the BLIT
[9] and the minBLEP [1] techniques;
