of Microprocessors

DIGITAL TONE GENERATION TECHNIQUES 471
index of all components of the complex modulating wave simultaneously. If
instead the calculations are restructured as in Fig. 13-26, the modulation
indices as well as the frequencies of each modulating component can be
separately controlled. Also, all table lookups remain into the same, easily
interpolated, sine table. As few as two modulating frequency components
have been found to dramatically improve the utility of FM synthesis. In one
experiment, piano tones (which are normally not well synthesized with FM
techniques) were quite successfully approximated using one modulating
ftequency equal to the carrier frequency and another four times the carrier
frequency. The slightly inharmonic partials of piano tones were then
simulated by slightly detuning these ratios.
"VOSIM"
Other "minimal-parameter" synthesis techniques besides FM are possible,
although none seem to be quite as flexible. One of these, which is quite
efficient in synthesizing a wide range of vocal-like sounds, is called VOSIM,
from the words VOcal SIMulation. VOSIM uses a very simple waveform
described by three parameters that is periodically repeated at the desired
fundamental frequency. Figure 13-27 shows the VOSIM waveform, which
consists of one or more bell-shaped pulses. A single width parameter specifies
the baseline widths of the pulses. The first pulse has unity amplitude, while
succeeding ones are smaller according to a decay parameter that ranges
between 0 and 1. Finally, a number parameter specifies how many pulses there
are in each period. Any time left over between the end of the pulse group and
the beginning of the next period is filled with zeroes. The pulses themselves
are sine-squared curves, which is equivalent to one cycle of a negative cosine
wave raised up to the axis. After the pulse group is specified, it is simply
repeated at the desired frequency and multiplied by an amplitude envelope.
Note that the time occupied by the group is in absolute terms independent of
the period. Thus, the "blank" time between pulse groups will vary with the
period, but the pulse group itself will remain constant. Ifthe period becomes
smaller than the group width, the group is simply truncated and restarted,
although this is normally kept from happening.
Figure 13-28 illustrates some of VOSIM's properties. Figure 13-28A
shows a reference VOSIM waveform (decay = 0.8, width = 1 msec, number
= 6, period = 10 msec = 100 Hz), along with its normalized harmonic
spectrum and spectral envelope. Figure 13-28B shows a wave with the same
parameters but with its period increased to 20 msec. Note that the overall
spectral envelope is essentially unchanged; there are just more harmonics
filling the space under it. Thus, the position in frequency of major spectral
envelope features remains constant as fundamental frequency is varied, a
desirable property not possessed by the digital synthesis techniques discussed
so far. Figure 13-28C shows that reducing the width parameter to 0.67 msec
increases the frequency of the broad spectral peak to about 1. 5 kHz. In Fig.
13-28D, the decay parameter is reduced to 0.5, which makes the spectral