[sdiy] Walsh update

[Neil Johnson]

Guys,

Thought I'd drop in on this thread :-)

> It seems that you would want each note within an octave and each octave to
> have the same timbre.

Oh, now, where's the fun in that?  How about being able to modify the
timbre depending on pitch?

> But, with the walsh generator you would want to freely manipulate the
> timbre, maybe through time. How are going to do that?

Using drawbars/pots/sliders/whatever to directly mix the Walsh functions
is bad medicine.  Much better to generate control voltages, and use those
to set the levels of each Walsh term.  Opens up a number of possibilities:
- set the basic spectrum (say from a micro + DAC)
- use front panel controls (sliders/bars/etc) to deviate from the default

> Wouldn't it be cool to convert from Walsh to sine series and have sine
> octave draw bars?

Erm... there is no simple mapping from sine (Fourier) to Walsh -- you'd
need an infinite (well, ok, band-limited) set of Walsh functions to
approximate a sinewave, and vice-versa.  But it is a neat idea to be able
to modify the harmonics while playing :-)

> The Walsh series would be longest for the lowest octave of notes but
> be very short for the highest octave unless your TOG is 32 or 64 times
> the highest note to be played.

The recommended minimum number of Walsh coeffs for synthesis is 32 terms
(comparable to LPF samples), so that should be sufficient for the entire
range, although of course if we're using FPGAs then we can do a lot
better.

In fact, if we are doing it in an FPGA, why not do all the maths inside an
FPGA altogether.  The slide bars could be sampled and fed in as digital
data, and the IWT performed entirely in the digital domain.  The output
could then be a serial stream for feeding straight into a DAC.

(I'm on a roll now)

So if we're in this midst of hundreds of thousands of gates, why not
multiplex the entire thing and create a polyphonic, multitimbral Walsh
synth engine?  Mmmm...tempting :-)

Ok, have I been thinking about this in the past?  Yes.  Have I done much
about it yet?  No.  My rate of progress on projects could be measured in
geological units :-(

But its nice to exercise the ideas once in a while.

Neil

--
Neil Johnson :: Computer Laboratory :: University of Cambridge ::
http://www.njohnson.co.uk          http://www.cl.cam.ac.uk/~nej22
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