## [opendtv] Re: Math of oversampling

• From: Mark Schubin <tvmark@xxxxxxxxxxxxx>
• To: opendtv@xxxxxxxxxxxxx
• Date: Fri, 22 Apr 2005 13:20:06 -0400

```>If a broadcaster uses a 1080p camera and broadcast as 480P and on the
>reception end it is upconverted to 720P or stays 480P I understand that
>because of oversampling both the 720P or 480P image would be better than
>otherwise would be expected. What I would like to do is quantify this
>value. How would you compare a straight thru 720P broadcast to one such
>as that above. Would the 1080P>480P>720P route be 75% of the quality of
>the 720P>720P>720P route? Would 1080P>480P>480P be 110% of 480P>480P>480P?
>
>

The calculable quality is not betterness but potential sharpness.  The
psychovisual sensation of sharpness is proportional to the square of the
area under a modulation-transfer-function (MTF) curve, a curve plotting
contrast ratio against detail fineness.  There are many factors
contributing to the function (lens, aperture, etc.), but, for the
purposes of your question, two "all-else-being-equal" (meaning an HD
lens on an SD camera)  factors will affect the sharpness: the number of
samples in the imaging chip and the optical low-pass filtering.  Even
dealing with just the former involves significant math:
http://www.cs.virginia.edu/~gfx/Courses/2003/ImageSynthesis/scribed_notes/09_sampling.pdf

I understand that I can't include attachments on this list server, but,
if anyone wants a diagram of the various contributions to MTF, contact
me directly, and I'll send it.  It's only about 70 KB.

TTFN,
Mark

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