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RE: [OM] A conspiracy?-another correction

Subject: RE: [OM] A conspiracy?-another correction
From: "George M. Anderson" <george@xxxxxxxxxxxxxxxxxx>
Date: Sat, 15 Mar 2003 07:59:18 -0800
Nyquist frequency and aliasing

Sorry, Jan but Joe and John were correct.

Here's a page I found with a rather simplistic, but effective illustration:

http://www.efunda.com/designstandards/sensors/methods/DSP_Aliasing.cfm#alias
ing
and another
http://www.opus1.com/~violist/help/nyquist.html

Sampling at a high rate can cause problems too, but as stated before, a low
pass filter in the signal path before sampling can solve those rather
handily.

George

PS: In fact, your example below IS an example of undersampling.  The Nyquist
theorem says you need to sample at at least 12.4 KHz to recover your 6200 hz
input signal.

PPS: So I think scientifically and as a matter of educated speculation,
there's no such thing as a 'too-sharp' lens. As long as the engineering
weeds out any potential 'bad' effects for the particular system in use.

>
>********************
> >From: Joe Gwinn <joegwinn@xxxxxxxxx>
> >
> >Aliasing is a consequence of the loss of information due to the
> resulting undersampling (too few samples to fully capture the image).
>**********************

Jan says:

> Someone has probably already jumped on you for this, but it is
> actually the opposite: sampling at too high a frequency such that
> sampled frequencies above the Nyquist limit (1/2 the sampling
> frequency) are included in the sampling. They then cause
> heterodyning artifacts, similar to well-known Moire effects.
>
> It's easier to comprehend in 1-dimensional space than 2D.
> Consider a very bad CD recorder/player that samples audio
> frequencies at a 10,000 Hz rate. If you feed the recorder an
> audio frequency of 6,200 Hz, the player will produce equal
> amplitude frequencies of 3,800 and 1,200 Hz -- not at all what
> was intended, and pretty awful sounding.
>
> This is what so-called "grain aliasing" is all about: scanning at
> a frequency that is near the RMS grain frequency of the image.
> Whereas if one scanned at a much lower frequency, it would
> accurately reproduce whatever it picked up, without ugly
> non-harmonic components.
>
> Audio (and other 1D sampling systems) include a low-pass filter,
> to keep frequencies near the Nyquist limit from producing
> sampling artifacts. CCD scanners have no such capability,
> although drum scanners perform low-pass filtering by varying the
> illuminated aperture that is sampled.
>
> So yes, a lens CAN be "too sharp" for digital, if it allows
> spatial frequencies at or above the Nyquist limit to be sampled.
> If your lens resolves (for example) 150 lpmm, but your sensing
> elements are placed very much farther apart than 300 lpmm, you'll
> have aliasing artifacts.
> --
> : Jan Steinman -- nature Transography(TM): <http://www.Bytesmiths.com>
> : Bytesmiths -- artists' services: <http://www.Bytesmiths.com/Services>
>
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