ODP: AW: Harmonix content formula

[Roman Sowa]

This is all true. And not only true for 'my device', but for every
spectrum analyser. Spectrum leakage problem is common not only
to the solution I proposed. We both agree it suffers from windowing
problem. Another point - with 'my device' there's no way to make
analysis in overlaping segments.

Roman

> -----Oryginalna wiadomość-----
> Od:	Martin Czech [SMTP:martin.czech at intermetall.de]
> Wysłano:	9 czerwca 1999 15:37
> Do:	synth-diy at mailhost.bpa.nl; Roman.Sowa at WizjaTV.pl
> Temat:	Re: ODP: AW: Harmonix content formula
> 
> > 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).