[sdiy] Walsh bank, was: Re: [sdiy] Micro as a Linear to Exponential converter?

[cheater cheater]

Neat. Or how about making the 'coefficient source' as in your example
(the DC voltage going into the DCA) come from an analog source, so
that you can patch an audio-rate signal? Now that could be interesting

And remember that you can make a DC source that's drifty, too. Digital
math with analog properties? Yeah!

D.

On Sun, Aug 16, 2009 at 9:38 AM, Magnus
Danielson<magnus at rubidium.dyndns.org> wrote:
> Michael O'Bannon wrote:
>>
>>>
>>> The great advantage of Walsh over Fourier is that coefficient
>>> multiplication turns into add or subtract.  Sinewaves you need to do
>>> multiplications all over the place (or that double-add-with-phase-shift of
>>> Hal Alles).
>>>
>>
>> With Walsh functions, don't you still have the final burden of adjusting
>> the amplitude each of function to get the desired mix of partials?  Is there
>> a way to do this in code without multiplication?  (I'm hoping the answer is
>> yes, but I haven't found a way yet.)
>
> Yes, but the point is that the walsh functions produces +1/-1 results rather
> than values between +1 and -1, so multiplication does not require a full
> multiplier but a very simple op-amp setup with a CMOS switch which switch
> the gain between +1 and -1. These DCA (Digitally Controlled Amplifier) is
> controlled by the digital walsh generator and the analog input is the
> coefficient. The output of all DCAs is added to form the full set.
>
> A fourier type of response using walsh generators could be achived using
> some math transforms..
>
> x(t) is the time-representation of a waveform
> X(f) is the fourier frequency representation of a waveform
> X(w) is the walsh frequency representatio of a waveform
>
> Fourier transform:
> X(f) = DFT(x(t))
>
> Inverse Fourier transform:
> x(t) = IDFT(X(f))
>
> Walsh transform:
> X(w) = DWT(x(t))
>
> Inverse Walsh transform:
> x(t) = IDWT(X(w))
>
> Consider that we want the walsh coefficients, but have the Fourier
> coefficients... then
>
> x(t) = IDFT(X(f))
> X(w) = DWT(x(t)) = DWT(IDFT(X(f))
>
> Thus, a new linear transform is formed from Fourier coefficient to Walsh
> coefficients. This new transform can be calculated in advance and could be
> calculated in N^2 multiplications and N(N-1) additions. However, both DWT
> and IDFT can be done efficiently, so just doing the transforms can be used.
>
> Just a little bit of linear transform math. Can be done in advanced in the
> processor, and the coefficients can be output through a DAC and regularly
> updated to S/Hs.
>
> Cheers,
> Magnus
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