[Tig] Nyquist/Fourier (was: new on the TIG wiki)

[Jack James]

but pixels themseleves are just samples, there is limited value in
reconstructing a perfect edge of a sample. in addition, ultimately the
limiting factor is the eye, which has a rough resolution of 500x500.
higher resolutions than 1000x1000 therefore only have an impact on the
ratio of viewing distance/screen size.

Jack

On 11/05/07, Joe Owens <jpo at prestodigital.ca> wrote:
> Thanks to Cedric Lejeune for support in 2007.
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>
> Without going to the wiki definitions, sampling theorem, as I learned
> about it 30 years ago, postulated that any signal wavetrain could be
> reconstituted (at least theoretically) by sampling it at a minimum of
> 2x the highest "resident" frequency.  That target frequency could be
> estimated by building that shape out of pure sinusoidal waves...
> (Fourier Transform).  For example a perfect square wave (definitely
> not sinusoidal) has to be built of a theoretically infinite number of
> harmonically related (odd) sines -- this is an elementary exercise in
> Engineering Physics at the 300 level, or at least used to be.  In
> other words,  there is no limit to the required sampling frequency to
> do a perfect mathematical reconstruction of something that has a very
> high spectral content.
>
> Engineering/economic practice, though, shows that you can get within
> a useful  range of the target by going up to about the 2nd or 3rd odd
> harmonic 5x or 7x base frequency (for a complex shape like a square
> pulse).  You get a kind of squarish, slightly rippling thing that you
> can re-shape on the other end, albeit with a little bit of lag...
> So for TV lines... are they sinusoidal?  If you wanted sharp
> squares... lets see now, for 1000 lines...  that means base frequency
> of (just for envelope calculations) 1000 "cycles"... go out to the
> second odd harmonic, make that 5000 "cycles"... double that for
> Nyquist... minimum sampling frequency 10K.  14K if you want another
> few per cent of resolution -- your edges will stand up a little
> straighter, and your circles will be a little rounder.
>
> Set me straight if I have this wrong....
>
> Joe Owens
> Presto!Digital Colourgrade
> 302-9664 106 Avenue
> Edmonton, Alberta T5H0N4
> +1 780 421-9980
> jpo at prestodigital.ca
>
>
>
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