16/44.1 vs Oversampling

[PeterSt]

"An oversampling DAC makes sines of squares, and therewith loses precious data (harmonics);"

 

and

 

"An answer to this false statement would need a lengthy article on the basics of D/A conversion and reconstruction filters"

 

Hi Daniel,

 

Can you please tell me which part in my statement is false ?

In fact you can only refer to the last part ("loses precious data (harmonics)") because the first you can measure yourself and this is just true. With this as a base I don't see how that second part could be otherwise.

 

I don't see what to get from the link you gave, but thanks for your additional explanation. Nothing wrong with it as I can see. However, I was not talking about that at all (aso see above response to Max).

 

"A multibit converter can also be sigma delta, actually the modern sigma delta converters are multibit, e.g. 5 bits."

 

I can't tell why you say this, because it will still be - and need oversampling. Or ?

That's why I said "equal to the number of output bits" (similar). Those do not.

 

Thanks,

Peter

 

[Roseval]

Daniel,

thanks for the clarification

 

[Max]

Daniel

 

In the case of 44.1 to 88.2 there is just one such filter required, i.e. the one which calculates the sample which is in between two 44.1 samples in order to get to the 88.2 grid of samples.

 

This is only true for ideal Lagrangian interpolation where the interpolating polynomial passes through the data points. You can't do Lagrangian interpolation in real life as the equivalent filters are infinitely long. Instead you have to use some sort of approximation, with a finite transition band. This filter MUST be applied to all output samples, including those which "don't need to be interpolated" or the frequency response of odd & even output samples will differ.

 

I don't know (not being in the industry) whether this sort of issue might be behind some of the 'DAC sound' comments we see about.

 

I'd welcome your comments

 

Max

 

P.S. - I have in the past designed true asynchronous SRC's for a living, but not in digital audio

 

[Max]

Peter

 

Sorry about the tag error - I hope this is OK now!

 

In a 44.1ksps PCM system, the Nyquist frequency is 22.05kHz. Hence for any frequency above 1/3 of this, i.e. 7.35kHz, a sine wave and a square wave will produce exactly the same bits. 12kHz was just an example. (Note: the lowest harmonic present in a square wave is the third).

 

If you are talking about preserving harmonics present in the original source, the only recourse is to increase the sample rate of the entire PCM channel, e.g. to 88.2ksps, and adjust the AAF & reconstruction filter bandwidths accordingly. Up/down sampling cannot recreate harmonics that were removed by the AAF.

 

Furthermore, what I said is that an NOS DAC retains squares where they were there in the source, while the OS DAC makes sines of it.

 

How can you tell? The original source might have had those harmonics in it, but it might not. The PCM data would be the same.

 

Max

 

[weiss2496]

An oversampling DAC makes sines of squares, and therewith loses precious data (harmonics).

 

Upsampling (or oversampling fo that matter) starts with a signal sampled at e.g. 44.1. That signal has harmonics up to a maximum of 22.05kHz, i.e. the Nyquist frequency, but in practice, the A/D converter used to generate that signal applied some anti-aliasing filtering and thus the usable band is likely to go up to 20kHz.

Upsampling to e.g. 88.2 kHz is done by inserting a zero valued sample between each 44.1kHz sample (so called zero filling) and then lowpass filter the resulting signal with a filter which has a passband up to e.g. 20kHz (i.e. what you would call the audio band) and a stop band which starts at 22.05kHz. So the audio content before and after upsampling is the same. No harmonics taken away. Just the images because of sampling are shifted to different frequencies. But those images are not harmonics and are unwanted signals and are cut off after the D/A converter in the reconstruction filter.

 

"A multibit converter can also be sigma delta, actually the modern sigma delta converters are multibit, e.g. 5 bits."

I can't tell why you say this, because it will still be - and need oversampling. Or ?

That's why I said "equal to the number of output bits" (similar). Those do not.

 

I said it just to give a complete picture. Yes they need to be oversampling in order to be able to shape the noise out of the audio band. "Number of output bits" in context of a sigma delta converter is kind of misleading. Or what are you meaning with that?

 

Regarding 44.1 to 88.2 conversion:

This filter MUST be applied to all output samples, including those which "don't need to be interpolated" or the frequency response of odd & even output samples will differ.

 

Yes, that is true. Just wanted to keep it simple....

 

Daniel