Waveshaping
Waveshaping is one of the abstact algorithms. Developing of waveshaping was started
in the end of seventieth.
The idea of this method id shown at a picture below.
 |
DESCRIPTION:
|
A sine generator is a source of a signal x(t)=cos(wt).
Harmonic signal is an argument in waveshaping function block. Waveshaping function f(x)
must vary in limited range. The envelope generator (EG) allows to get more realistic character
of a sound synthesized instrument. Without EG can get only a constant in time
frequency spectrum of a sound, that is a steady state. Synthesis of sound in waveshaping
is doing in two stages. In a first stage is executing spectrum analysis of a natural sound
to determined proportion between harmonics. In a second stage is calculating - on the
basis of results got during first stage - a wavashaping function.
To determine a waveshaping function the Chebyshev polynominals are used:
 |
 |
 |
A result of transform sine signal in waveshaping function equal to
Chebyshev polynominal k - order is k - order harmonic of this sine signal.
Whole waveshaping function is get by sum n Chebyshev polynominals in
proportions determined during first stage, where n is a number of
harmonics which we would like to synthesize.
A main advantage of waveshaping method is small compute complexity
and ability to analitical determine a waveshaping function for a
quasi-steady states. A disadvantage of this method is that is very complicate
to synthesize a transient states. Waveshaping also does not allow
to direct synthesize a nonharmonic sounds.
One of a most popular instrument which uses waveshaping to synthesize
sounds is Korg 01W.
Sound examples
 |
||
 |
bassoon - natural soundFrequency spectrum of instruments
Go back
Phase distortion method belongs, similarly to waveshaping, to abstract
algorithms class. The idea of this method is dynamic changing phase of sine signal.
In this method a sine generator is a wavetable oscillator. Phase distortion is
doing by retrieve the samples of sine wave stored in memory at different
rates of speed. It is important to call up all samples at different speeds within
one wave cycle. This distorts the relative phase points of the wave,
and in fact, generates a whole new waveshape. Fundamental frequency of
a sound is equal to frequency signal from oscillator.
It is shown at a pictures below.
In fact, author of this research knowns only one instrument which uses phase distortion method to synthesize sounds: Casio CZ series. The following text describes solutions implemented in that instrument.
Block diagram of Casio CZ series
Generator block is call Digitally Controlled Oscillator, in short
DCO. Low Frequency Oscillator (LFO) was implemented
in this instrument to allow vibrato effect. LFO can control a DCO block.
Phase modulation is doing in DCW block (Digitally Controlled Waveshaper).
User has full control over a deep of phase distortion and in this way
over a timbre of sounds. Signal from DCW is send to DCA
(Digitally Controlled Amplifier), where a final volume is set in depend of key speed.
It is important that every block: DCO, DCW and DCA, contains independent
an envelope generator (EG). It allows to synthesize sounds with very complexity envelope.
One sound come into two separately paths DCO-DCW-DCA. These paths are call lines.
Output signals from every lines are send to detune block. Detuning may be
used in small amounts to generate beating effects or in large amounts to produce two
distinct pitches.