PHYSICAL AND BEHAVIORAL CIRCUIT MODELING OF THE SP-12
SAMPLER
David T Yeh, John Nolting, Julius 0. Smith
Center for Computer Research in Music and Acoustics (CCRMA)
Stanford University, Stanford, CA
ABSTRACT
Aliasing, usually considered an artifact of discrete time
systems to be avoided, is found to be an aesthetic feature of the E-MU SP- 12 sampler/drum machine. This paper presents the steps in modeling the SP-12 as a signal
processing system. Measurements of the characteristics
of the SP-12 are presented. The signal path is analyzed
to produce a physically based model of the circuit. Circuit analysis in SPICE provides transfer functions, which
are converted into digital filters by system identification.
Aliasing is implemented using interpolation and downsampling. The results of the algorithm are compared to
samples from the original system.
1. INTRODUCTION
Physical modeling is an approach to deriving efficient
algorithms to simulate various signal processing circuits.
Sometimes a physical model is too involved to implement
directly, but its insights are used to derive a behavioral
model that approximates the correct response. This is
sometimes termed virtual analog circuit modeling. A
combination of reverse engineering and circuit analysis
allows the systematic formulation of an algorithm that
faithfully reproduces the character of the original system.
In this paper, these techniques are applied to the E-MU
SP-12 sampler/drum machine to create an algorithm that
reproduces the sound of this device, which is no longer
being manufactured.
1.1. Features of the SP-12
The SP-12 (Sampling Percussion), introduced in the mid80s, is a sampling drum machine with a sequencer to lay
down drum tracks. It features 8 velocity-sensitive pads, 8
control slides, and 8-voice polyphony through 8 independent outputs. It samples at a low 12 bits and 27.5 kHz rate.
The Turbo version features 192 kB of wavetable memory,
which is about 5 seconds, but each waveform can only be
a maximum of 2.5 seconds. It features MIDI interfacing
and SMPTE synchronization. There are 24 internal waveforms stored in ROM, and 8 slots that the user can record.
Each output channel features a different equalization. The
interface allows users to edit samples by looping, truncation, and adjusting the decay.
Figure 1. Control panel of the E-MU SP- 12 sampler.
The SP-12 is used for hip hop beats, to give drum
sounds a hard edge and grit. A rudimentary pitch shifter
can detune sounds, but also adds a gritty character that
comes from aliasing. It also features a warm low-pass
equalization that musicians desire.
1.2. Background material
Literature in virtual analog often discusses alias reduction.
Efficient methods of generating bandlimited waveforms
for subtractive synthesis are described in [7, 9].
The canonical virtual analog example is the Moog filter
[8, 1]. This work extends upon that earlier work, integrating the analysis of the components into the modeling of
an overall system.
2. OVERVIEW OF THE SP-12 SIGNAL PATH
The SP-12's signal path consists of an anti-aliasing filter
based on operational amplifiers (opamps), a sample and
hold at 27.5 kHz, a 12-bit successive approximation quantizer, time-domain digital signal processing, a zero-order
hold (see p3.4), and a choice between six optional equalization filters to attenuate spectral aliases from the zeroorder hold. Two of these filters employ the SSM-2044
Voltage Controlled Filter (VCF) chip as a 4-pole lowpass
with time-varying cutoff frequency.
The time-domain processing of the SP-12 features
variable-decay time-enveloping of the signal, and a rudimentary pitch shifting algorithm common to digital synthesis systems of that era [7].
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