AW: additive

[Eli Brandt]

David MOYLAN wrote:
> Now for the tough part: figure out a formula analogous to the
> Fourier Transform but for triangular components.

I tried to do the deconvolution to get the triangular spectrum of a sine.
Even after fixing the sign errors in my last post, I still had to hack the
signs some more, and the resynthesis doesn't seem to _quite_ converge.  So
I'm not putting the (Matlab) code up, though I'll mail it if you want to
fix things.

Anyway, here's a trispectrum, out to 64, that seems to work pretty well.
Use the FFT to get your signal's sine-harmonic series, then convolve with
this to get a tri-harmonic series:

 1.0000000e+000 0.0000000e+000 -1.1111111e-001 0.0000000e+000
-2.7654321e-002 0.0000000e+000 -1.2891016e-002 0.0000000e+000
-7.5395973e-003 0.0000000e+000 -4.9749731e-003 0.0000000e+000
-3.5400341e-003 0.0000000e+000 -2.6530804e-003 0.0000000e+000
-2.0652085e-003 0.0000000e+000 -1.6548627e-003 0.0000000e+000
-1.3567445e-003 0.0000000e+000 -1.1331476e-003 0.0000000e+000
-9.6102572e-004 0.0000000e+000 -8.2563102e-004 0.0000000e+000
-7.1716096e-004 0.0000000e+000 -6.2888900e-004 0.0000000e+000
-5.5607210e-004 0.0000000e+000 -4.9528640e-004 0.0000000e+000
-4.4400919e-004 0.0000000e+000 -4.0034788e-004 0.0000000e+000
-3.6285975e-004 0.0000000e+000 -3.3042918e-004 0.0000000e+000
-3.0218235e-004 0.0000000e+000 -2.7742681e-004 0.0000000e+000
-2.5560804e-004 0.0000000e+000 -2.3627769e-004 0.0000000e+000
-2.1907000e-004 0.0000000e+000 -2.0368421e-004 0.0000000e+000
-1.8987112e-004 0.0000000e+000 -1.7742283e-004 0.0000000e+000
-1.6616475e-004 0.0000000e+000 -1.5594941e-004 0.0000000e+000

-- 
     Eli Brandt  |  eli+ at cs.cmu.edu  |  http://www.cs.cmu.edu/~eli/