How does DSD to PCM conversion work?

[Soria Moria]

Hi, newbie here. I've seen a lot of PCM music that has been converted from DSD64, and what they seem to almost always have in common is that the PCM converted version is 24-bit 88.2 KHz sample rate. From what I know of DSD and specifically DSD64, is that it's 1-bit at a 2.8224 MHz sample rate. So why do they choose 24-bit 88.2 KHz? How can you get 24-bit out of only 1-bit? And aren't they leaving a ton of sample rate at the table? Wouldn't it work to convert it to 24-bit 786 KHz?
Thanks in advance!

 

[Elitzur–Vaidman]

24bits per sample * 88,200 samples per second = 2.1168Mbps
1bit per sample * 2.8224 MHz sample rate = 2.8224Mbps

 

[pkane]

How can you get 24-bit out of only 1-bit? And aren't they leaving a ton of sample rate at the table? Wouldn't it work to convert it to 24-bit 786 KHz?
Thanks in advance!

Conversion from 1-bit DSD to PCM is fairly easy, it just requires a low-pass filter and down-sampler/decimator to convert to the desired PCM rate.

There's not much reason to keep the higher frequencies when converting from DSD64. Even if these frequencies were audible (which they are not), DSD produces a huge amount of quantization noise that is pushed out to those higher frequencies through noise shaping. With DSD64 that noise starts right above the audible frequencies. If you were to convert it to 768k PCM, you'll just be wasting bandwidth to store lots and lots of noise.

 

[formdissolve]

A lot of convertors use 24 bit / 176.4, but 88.2 is fine because they usually have a 30khz low-pass filter in place to filter out that quantization noise that pkane was talking about. 88.2 / 2 = 44.1, which is well above the 30khz low pass. It's in 24bit because 1 bit PCM would sound horrible. 1 bit works for DSD because it runs at a sample rate of 2,822.4 mhz instead of much lower 44.1 khz..

DSD64 is 64x the frequency of regular CD - 44.1 * 64 = 2,822.4 mhz
DSD128 is 128x.. etc

 

[DVDdoug]

How can you get 24-bit out of only 1-bit?

Well... A DAC converts it to analog which is "smoothed" and continuous, so equivalent to an infinite sample rate. (Actually there are NO samples because analog is not quantized.) Analog does NOT have infinite resolution! (Some people make that mistake.)

Or you can up-sample from 16/44.1 to 24/96 (etc.) by interpolating but of course that just increases the format resolution, not the underlying audio resolution or the sound quality.