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