DCO's, Anti-Aliasing, and Filters

[Rob]

ANY and ALL digital signals have aliasing...There is no way around it.
This is because between the samples, or dots that represent the
waveform, ANYTHING can happen, and we would never know about it from the
digital recording. This is really where aliasing occurs. Its about the
space between the dots.

We say that this is a straight line, but more often, it is not. The
natural curve of the original analog signal is gone.

The best way to describe aliasing is to think of what aliasing means in
dictionary terms:something is acting or taking on the characteristic of
something else.

In our terms, it means that there is insufficient numerical frequency to
accurately represent all the harmonic characteristics of our original
information. 

So, what happens is that we have a recorded signal that has all the
elements to represent a harmonic below the information. Like not having
enough dots when playing connect the dots.. If you dont have enough dots
to accurately represent your image, you could think that a picture of a
cow was a teacup.. This is in essence what aliasing is.
In the picture example, the dots are represented in x and y, whereas in
our example, they are represented by y vs. time.

So, from what I have seen, all anti-aliasing filters do is limit
bandwidth. The anti-aliasing filter is a bandpass filter with a steep
rolloff after the upper and lower limits of our hearing (10hz to 25khz)
that makes the aliasing inaudible, or at least lessened..
But, if you did not record with sufficient sampling rate essentially you
are just going to make muddy semi-sinusoidal noise. Try it sometime..
I hope this helps anyone who was lost in the shuffle of the discussion.

Rob

Anyone who is interested, correct me if I have made a mistake. :)