DCO's, Anti-Aliasing, and Filters

[Beszedes Arpad]

Hi!

Rob wrote:
> 
> 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.
> 

One way to improve this is the following technique which is used in
software (or even some hardware) wavetable synthesis: you do not
determine the actual output voltage based only on the two surrounding
samples (i.e. a straight line, which is actually a 1st order (linear)
interpolation), but you take into account >2 of the surrounding samples
(say 4), and this is in mathematical terms called an nth order
polynomial interpolation. Of course the accurate reproduction would
require all of the samples (which are sampled on the Nyquist frequency,
i.e. 2x the highest harmonic in the input analog signal), but this is
based on the calculation of the DFT (Discrete Fourier Transform) of the
input samples, so it's interesting only in mathamatical theory.


> 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. :)

-- 
***********************************************
*  Arpad Beszedes                             *
*                                             *
*  Research Group on Artificial Intelligence  *
*  Hungarian Academy of Sciences              *
*  Attila Jozsef University, Szeged, Hungary  *
*  e-mail: beszedes at cc.u-szeged.hu            *
*  tel.: (+36) 62/45-41-45                    *
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