wavetable FM !

[mbartkow at ET.PUT.Poznan.PL]

Dear all,

as I was thinking about ADC-based wavetable generator, and especially
about phase unwraping, I realised suddenly that unwraped and rewraped
phase is what is exactly needed for the FM synthesis a'la Yamaha.
In the simplest case (a sine carrier and a sine modulator), 
their modulated wave may be expressed as:
y(t)=A*sin(2*pi*f1*t+I*sin(2*pi*f2*t)), where I is the modulation
depth. What made FM synthesis famous is the possility to nest
the modulators, and to change the depth I in time.

While it was allways very tempting to develop the FM algorithms
in analogue synthesizers, the tracking problems of frequency modulated
VCOs are the most distracting. Now, wavetable synthesis offers the
post-VCO FM possibility (to be more precise, it is rather a phase
modulation, but I am using Yamaha's terminology here) with true
through-zero modulation possibilities.

Imagine an additional input to the Wiard waveform city circuit. This 
input is directed to a bipolar ADC. The outputs of the both ADCs are
digitally added and used as an address to the wavetable. We can 
harmlessly neglect the carry mark, since the wavetable contains 
exactly one cycle of the waveform. In fact, dropping of the carry
mark is just responsible for the above mentioned phase rewraping.
The modulation depth is limited and depends on the ADC resolution 
and the way the numbers are added. For example, having the second
ADC 10-bit and neglecting the 3 most significant bits of the digital
sum, we achieve the modulation depth range as big as +/- 8PI which
is comparable to what DX-7 offered, AFAIK.

Having few stable and well-tracking VCOs (maybe V/Hz for better
performace, as JH suggests) and few ADC-based wavetable shapers it
is possible to recreate all the famous Yamaha FM algorithms, and
more - we are not limited to sine waves.

I have an old TX81Z module which features other wave shapes and it
offers a remarkable palette of timbres. The problem is aliasing, since
the internal sampling rate in Yamaha FM synths is not very high.
Here we have very high sampling (400kHz in case of Wiard's design)
and that should be no problem.


Well, let me only say, now I am ultimately converted to Grant's
point of view.

regards,

mb


--

Maciej Bartkowiak, PhD
========================================================================
Institute of Electronics and Telecommunication     fax: (+48 61) 8782572
Poznan University of Technology          phone: (+48 61) 8791016 int.171
Piotrowo 3A                             email: mbartkow at et.put.poznan.pl
60-965 Poznan POLAND               http://www.et.put.poznan.pl/~mbartkow
========================================================================