ODP: AW: Harmonix content formula

[Martin Czech]

> convolution - I agree, but look at it this way:
> frequency bin coefficient is an integral taken over whole sine period
> of multiplied input and sine (or cos). Lets assume we calculate only
> those coefs derived from cosine waves. So instead of mentioned
> envelope followers (shortcut thinking mistake) integrators would be
> required, which outputs are sampled at the end of fundamental cycle
> and then the integrators are reset.
> 

Let's see.
I assume that a sine wave is fed into your device. If the frequency
of the input wave and the analysis sine wave is the same, modulation
(well multiplication) gives dc offset (this is the desired value and
double frewquency (this will vanish via integration). Seems to work.
If we take Fin=2*Fanalysis we will only get ac components, they too will
vanish via integration. Orthonormal functions.  Now we take some odd
frequency ratio, and the integration over one cycle will fail.  The ac
components will not vanish, the integration has to be extended to +-
infinity in order to do this.

I think this is the windowing problem seen from the other side.

So for random input your proposed device seems to have problems,
it will not really give use a FT.

> You say, that I see FT like filtering with sine impulse response filter...
> Convolution with sine IS filtering with sine impulse response filter.
> 
I just wanted to say that FT is equivalent to filtering (of course a
non realizeable filter).