Re: TOTALLY OFF TOPIC: 24-bit-per-pixel limit to Gdk RGB ?

[individual <individual mi cl>]

On Wednesday, February 19, 2003, at 07:02 PM, TORRI Vincent wrote:

> On Wed, 19 Feb 2003, individual wrote:
>
> > On Wednesday, February 19, 2003, at 12:06 PM, TORRI Vincent wrote:
> > > > > http://www.yorku.ca/eye/machband.htm
> > >
> > > One thing about this link : the fact presented at this link looks 
> > > like
> > > the
> > > Gibbs phenomenum in the Fourier analysis. Quite interesting, as we 
> > > can
> > > consider that the eye make a Fourier transform, according to some
> > > papers
> > > (the eye detects the wavelength (or the frequencies, as you want) of
> > > the
> > > colors)
> >
> > I seriously doubt it. The Gibbs "overshoot" appears in the frequency
> > domain, not in the spatial domain, which the lower graph represents.
>
> Well ? I don't think so : if you take one 1-periodic funtion which is 
> NOT
> continuous (called f), f(k) its kth Fourier coefficient and Fn(x) the 
> sum
> over k=-n to n, of f(k)exp(2iPikx), and if you display Fn, you will see
> the Gibbs phenomenum (L infty norm of f < a constant < L infty norm of
> Fn).
>   Take f(x)=0 for x in [0;0.5[ and f(x)=1 for x=0.5;1] (which is almost
> the function drawn in the page below) and draw Fn (n=50 for example). I
> will look (a bit of course) like that.If you take f as the black 
> function,
> and do the same computations, you draw Fn and you remark that Fn goes
> upper and lower than f (even if there is no Gibbs phenomenum in this
> case).

Yes, you are right.

>   My previous post was just a remark : the red curve let me think about
> the gibbs phenomenum. I don't know any link between Gibbs phenomenum 
> and
> the mach bands.

Ah, I see. In any case, I don't see how there could be a link, because 
the eye/brain does not do a Fourier transform of the light (to percieve 
the light's frequency), it only samples it at 3 electromagnetic 
frequencies. One could argue that there *is* a fourier transform going 
on inside the eye, but it has to do with the lens system. Anyway, you 
probably know all of this so I'll shut up now :-)

Paul