Question about # of bits fed to a DAC

[MtBiker]

So if a CD has 16 bit resolution, how do you use a 24bit DAC at all? Does the DAC take a 16bit word and interpolate it to 24bits before conversion?

Also, are DAC's hard wired at a particular sampling rate? I mean if I play a CD on a DVD player with 24bit/96kHz DAC's, what bit & sampling rates are used by the DAC in the conversion process?

TIA

[jwb]

DACs can be configured for different rates, and their input word format can be set to accomodate different word widths. Going from 16 to 24 bits is trivial: just shift left 8 bits, or use a left-justified word format.

Sample rate conversion is usually accomplished by a (gasp) sample rate converter. The usual technique is to determine the input and output sample rates, interpolate to the output, and apply a low-pass FIR or IIR filter to discard the image artifact.

In general a DAC chip doesn't care about the sample rate. It is only aware of the relationship between the bit clock and the word clock.

[MtBiker]

OK so I understand the left shift. Does the DAC chip itself do that or do people have to implement the shift operation themselves. So in essence, people are taking advantage of the extra bits but not the sampling rate because I've seen few upsampling DAC's.

- If you have a 192kHz capable DAC, it makes no difference unless you upsample (?)
- How do you build a DAC--actually how would you clock a DAC--that locks onto different sampling rates
- Where can I go to read about how upsampling is performed (what chips/processes), or to answer any of my other questions instead of bothering people on this forum?

[Werner]

Originally posted by MtBiker

- Where can I go to read about how upsampling is performed (what chips/processes),

Problem is, most of the stuff about this on the internet is dead wrong.

1) upsampling = oversampling

2) oversampling =

a) generate sample train at desired higher frequency, i.e. by inserting zero samples or by repeating samples (doesn't really matter)

b) apply steep low-pass filtering to this sample train with a cut-off at the *original* fs/2.

Remarks:

-phase a) is trivial when doing integer sample rate conversion, i.e. 44.1k to 88.2k. Less trivial when doing non-integer conversion, i.e. 44.1 to 96. That's why the latter is pretty dumb in the context of CD.

-phase b) when mathematically/politically correct one uses an approximation of the Shannon-prescribed Sin(f)/f filter. When inspired (but fundamentally wrong) one can pick just about any other funny filter.

-the output of the filter will be a sample train with higher wordlength, as digital domain filtering involves here the convolution of the 16bit signal with 12-24bit (?) coeficients, resulting in an internal representation of up to 48 bits. To avoid loss of information these ideally all have to be converted by the DAC, but since we are bound to this universe one dithers and rounds to 20-24 bits and then feed these to the DAC.