[sdiy] How does a DCO work?

[Richard Wentk]

At 13:16 30/12/2004, Paul Maddox wrote:
> > Or alternatively, are we talking about the same thing?
>
>no we're not, but we're close, an dthe distinction needs to be made..

Ok...

> > You can implement a phase accumulator with a fixed sample rate, in which
> > case you get aliasing just as you would in any other fixed sample rate
> > system. See e.g.
>
>Agreed, but no-one has yet mentioned the phrase 'fixed sample rate' in
>conjunction with 'Phase accumulator', which is why I said fixed sample rate
>systems need to be concerned with band limiting.
>Ok, this a bit of an 'untruth', see the end of the email as to why.

I got this. The issue for a PA system is what the clock rate is. Being 
picky, a PA system is still a fixed sample rate system, but for a typical 
hardware implementation the sample rate is very high. If you try to 
synthesize frequencies that approach the clock rate - as in the example - 
you'll get aliasing. But with a 10MHz clock and audio frequencies, it's not 
an issue.

The problem is that there are situations where a PA-like oscillator  - in 
the sense that you have a phasor going round and round based on accumulated 
phase increments and indexing into a table - is implemented at 44.1, or 
whatever, as happens in some softsynths. You're then dealing with a 
software simulation of a phase accumulator being clocked at a very low 
rate, and aliasing is the inevitable result, unless you attempt some form 
of band-limiting, or oversampling/decimation.

 From which there's the suggestion that if DSP based systems upped their 
clock rate well above the current limit of 192kHz, sound quality would 
instantly improve and you'd very likely lose all of the digital crunch and 
grit that mars current implementations.

I'd love to know what a 10MHz Virus sounds like. :-)

>The type of aliasing associated with fixed sample rates sounds a bit like
>ring modulation,

That's because it is a relative of AM. In any digital system you're always 
modulating your output signal with the sample rate, but the mirrored 
sideband is usually filtered out.

>So technically, it *is* possible to get aliasing (with discrete digital
>Phase accumulators) when using high output frequencies or very wide lookup
>tables. But with a sample rate of 10Mhz or more, you need to be an alien to
>hear any aliasing caused by this. For all practicle sense (ie, comming back
>down to earth) the aliasing doesn't exist.

Yep.

Richard