On Mon, 13 Feb 2012 15:13:49 -0000, "David J Taylor"

<(E-Mail Removed)> wrote:

>

>Many of the resolution tests showing a step-wedge chart apparently show

>aliasing at just less than Nyquist, but this is using a square-wave light

>pattern which has harmonics. Perhaps this explains what is being

>reported?

>

>Possible example:

>http://a.img-dpreview.com/reviews/Ca...84-ACR-003.jpg

>From: http://www.dpreview.com/reviews/canoneos600d/page11.asp

>

>David
That's entirely possible. Using the audio analogy, a frequency even

right at nyquist will have no in-band aliasing. When it's reproduced

it will be reproduced as a square wave, which has the fundamental plus

all of the odd harmonics, each diminishing in amplitude as you go up

in frequency. However, the reconstruction filter will take out those

odd harmonics and reproduce the original sine wave at nyquist. The

original signal *must* have been a sine wave for it not to have any

content above nyquist if the fundamental was right at nyquist. If your

original signal was not a sine wave, then it's frequency content above

nyquist will cause aliasing. This is the case you mentioned above.

While frequencies just below nyquist will have an alias just above

nyquist and frequencies close to 0 will have an alias close to the

sampling frequency, those aliases exist only mathmatically and they

are not reproduced during reconstruction. That's because

reconstruction only reproduces the lowest frequency of all the

possible aliases, of which there are an infinite number.

The problem with aliasing when sampling above nyquist is exactly due

to the fact that reconstruction only reproduces the lowest of the

aliases, which in this case is the wrong one. If all the content is

below or even right at nyquist, there will be no aliases reproduced

during reconstruction.

"nospam" may also be getting confused by what reconstruction filtering

is doing. It has to "smooth the jaggies" produced because you have

steps in the reconstructed signal but the original was probably

smooth. The high frequency content in those steps has nothing to do

with aliasing and they can be removed with a good reconstruction

filter while aliasing cannot be removed by filtering. That's because

the steps' frequency content is well out of band so you can filter it

with a lowpass filter. But the aliasing produced by undersampling is

in band so filtering it won't work because you'll also filter out part

of your original signal.

So in summary: There are no aliases reproduced from digital content if

all of the original sampled signal is at or below the nyquist

frequency. Not even a frequency "a little below nyquist" will cause

aliases to be reproduced. You're going to have to search long and hard

to find a reputable DSP textbook that says otherwise.

Steve