I2S and 16 to 24 and 32 bit conversion LSB extension errors

[RayCtech]

On the average the error on the lsb is 50%. Even if it were 100%, and for certain samples and converter architectures it may be, that's an error of 1 part in 65,536 for a 16-bit DAC, still 96 dB below full-scale, so I am not at all sure it is audible. It's kind of like dithering the noise floor. Which all delta-sigma designs do anyway so would mask this error.

1. With reference to full-scale I think 1 / (65,536 / 2) may be more correct as it is only the negative samples that is affected.
2. As the normal (average level) is maybe 20dB down from full-scale and the frequency spectrum normally slopes down with 6dB/oct in level from the 20Hz (bass area)- then the error / distortion level will be more dominant as the frequency rise than the otherwise "worst" component- the speaker drivers- the higher the frequency the more dominant the error / distortion will be- expect that 3kHz and up are where the real sonic impact hits.

 

[DonH50]

1. 1 lsb is referenced to the resolution, there are 65,536 (or 65,535 depending on the decoder) lsbs in the full-scale. Signing just introduces an offset to 0-center, does not change the reference. Either way I think the difference is very small; saying it is 100% of an lsb seems misleading even though it is certainly technically true.

2. Hmmm... Your argument is the error is more significant at higher frequencies because the signal level is lower, correct? Again, I would not argue that at all, but I would not use the word "dominant" and lsb in the same sentence. Just to approximate grossly, if we have 100 dB dynamic range (SNR for a 16-bit converter is ideally about 98 dB, SFDR about 144 dB, take your pick) and the average signal is a fairly modest -50 dBFS, then an lsb error is still ~50 dB below that. Again, I am not arguing the math, just the audibility. I certainly do not claim to hear what you can, but it still seems to me the error is very small. Most ADCs and DACs have other (larger) errors that will mask the sign error, and the lsb-level dither (noise decorrelation) signal usually added to a digital system will cover it.

Thanks for the discussion, don't think we'll convince each other but it is a good thing to make people aware.

 

[wizard1238]

If the I2S «standard» states that 0 padding should be used for both positive and negative samples.
then the DAC should be smart enough to detect the input I2S bit length and decode accurately?
or we can set the DAC input I2S bit length to avoid LSB extension errors, right?

 

[jkeny]

Can I play devils' advocate here - is this conditional padding correct?
I can't see what error it is correcting but I might be missing something
Don's simulation seems to deal with the differences between 24 & 16bit when the 8 LSBs have some signal in them rather than if they were just being padded out by 0s or 1s which is what the conditional padding is about.
Am I missing something?

 

[DonH50]

You brought up a year-old thread? If you mean the 8 lsbs of the 24-bit signal, IIRC (from a year ago) they are irrelevant. The last byte is padded based upon the 16-bit lsb. There was a fundamental concept that was missed and AFAIK long since resolved. The usual, easiest methods for dealing with truncated data are to either zero-pad or to fill out with the lsb of the smaller word size. More advanced algorithms use predictive coding to estimate what the lsb's would be based upon the other bits but that is not the topic of this thread.

The worst-case error no matter what you do is one lsb of the smaller word, not some massive error as the original claim.