🚀 go-pugleaf

In article <C0F8Hp.84n@ve7frg.ampr.org>, doug@ve7frg.ampr.org (Doug Collinge - VE7GNU) writes:
> If my CD with a "1 bit DAC" and the aid of "8 times oversampling"
> can produce audio as good as an older CD with no "oversampling" and
> a 16-bit DAC then can my circuit with an 8-bit DAC be replaced
> with a 1-bit DAC and 4-times oversampling?
> 
> How?  What's the math behind this concept anyway?

As far as I know the basic principal in over-sampling is to convert the digital
values into a PWM (Pulse Width Modulated) signal.

For 4-times oversampling you take 2 bits of data and generate a signal inside
the sample period to give the same average value as direct conversion e.g.:

0V ->  00(base 2) -> 0V 0V 0V 0V  =  0/4 = 0V
1      01         -> 0  0  0  4   =  4/4 = 1
2      10         -> 0  0  4  4   =  8/4 = 2
3      11         -> 0  4  4  4   = 12/4 = 3 
                     ^^^^^^^^^^
                     four samples of equal length

To get the 16bit value "0000 0000 0000 0010" from a 14bit DAC, you do two samples
at "0000 0000 0000 00" and two at "0000 0000 0000 01" at four times the 16bit
data rate. However as there is only one transition required it is not completely
necessary that the 14bit DAC is four times faster (but something has to work out
the transition time at that bandwidth).

I'm not sure what scheme the "1 bit DAC" actually uses, but the implication is
that you would need 256 times over-sampling for 8bits. 

Kev.
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