[sdiy] New and Improved Buchla waveshaper analysis

[Aaron Lanterman]

Here's my new rendition of the nonlinearity from the timbre circuity of 
the Buchla 259 Programmable Complex Waveform Generator:

http://users.ece.gatech.edu/~lanterma/buchla_nonlinearity.png

The original one I posted had a flat, zeroing part in the middle. That was 
due to me accidentally losing a resistor multiplier when I did the algebra 
on the analysis, which gave the nonlinear parts a gain of thousands of 
times greater than they should have been, hence swamping the direct part. 
Once I fixed that, I now get a nice "toothy" transfer function.

Someone posted a link to oscilloscope plots of the Serge wavefolder; I 
can't seem to find that link again, but this looks similiar to what I 
recall seeing, except I remember the Serge gave a more rounded transfer 
function.

Granted, I did my analysis based on assuming "ideal voltage starved op 
amps" - the real Buchla circuit might give a more rounded transfer 
function.

Here's my two new soundfiles:

http://users.ece.gatech.edu/~lanterma/buchla_timbresweep.wav
http://users.ece.gatech.edu/~lanterma/buchla_symmetrysweep.wav

In "timbresweep", the input offset is set to zero, and the amplitude of 
the wave is swept from 0 to 8 volts and back. In "symmetryswwep", the 
amplitude of the wave is set to 4 volts, but the DC input offset sweeps 
from 0 to 4 volts and back.

I made two plots to try to visualize the spectral content. To get 
something cleaner than a spectrogram typically is, I ran a loop where I 
varied one of the parameters; in each loop, I used just one cycle of a 
sine wave as input, and then ran an FFT on that, and then stacked up the 
results. In the below files, on the left you see a plot of the 1st, 3rd, 
5th, and 7th harmonic amplitudes (oops - for the symmetrysweep, I should 
have plotted the even harmonics also, I forgot) over time.

On the right, you see an image; from top to bottom is different harmonics, 
from left to right is time.

http://users.ece.gatech.edu/~lanterma/timbresweep_analysis.png
http://users.ece.gatech.edu/~lanterma/symmetrysweep_analysis.png

The parameters were varied as in the soundfiles, except they were just 
varied "one direction" - i.e. as in 0 to 4 or 0 to 8, but not back again.

Notice on the "timbresweep" analysis, that the various harmonics fade in 
and out, but the overall structure is that more harmonics get added as the 
input amplitude increases. If you listen carefully, you can specifically 
hear the pulsing of the fundamental, particularly the longer rendition of 
it near the middle of the soundfile (which you can see on the image plot).

Of course, with the symmetry offset set to zero, you only get odd 
harmonics. In the "symmetrysweep" analysis you can see the even harmonics.

Someone mentioned that this waveshaper was designed to emulate the effect 
of an FM modulation scheme. I haven't started to think about yet, but I 
suppose you could argue that the pulses you see in the harmonic amplitude 
plots look kind of like Bessel functions...

This was all done in MATLAB, which is my friend.

Oh... there's two effects in the actual C259 which aren't modeled here 
yet. One, is it seems that some of the original input is mixed directly 
into the output, entirely bypassing both the waveshaping AND the 
amplitude/offset circuitry that comes below the waveshapers. That probably 
alleaviates some of the "pulsing" you hear the fundamental doing. The 
other effect is it seems there's a single-pole lowpass filter on the 
output with a cutoff of around 1.3 kHz... maybe that's there to take some 
of the "edge" off the sound (and my soundfiles are pretty edgy!)

I'd like to do the same analysis of the Music Easel shaper - but I can't 
find the power supplies to the op amps!

- Aaron

-----------------------------------------------------------------------------

Dr. Aaron Lanterman, Asst. Prof.       Voice:  404-385-2548
School of Electrical and Comp. Eng.    Fax:    404-894-8363
Georgia Institute of Technology        E-mail: lanterma at ece.gatech.edu
Mail Code 0250                         Web:    users.ece.gatech.edu/~lanterma
Atlanta, GA 30332                      Office: GCATT 334B