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# DSD vs. PCM

#1

Ted Smith, lead designer of DirectStream and the architect of how it works inside, explains DSD and the differences between DSD and PCM. In this short video, you get to learn a little more about how it works and why DirectStream sounds the way it does.

#2

Thank you, Paul and Ted!

“Hear everything on your recordings” is a nice tag line.

#3

+1 A good expansion on previous discussions of PCM versus DSD. Much appreciated.

#4

Let’s see if I got this right, Ted says 1 bit has 6 dB of signal to noise ratio (S/N). So when you have a 16 bit system you have 96 dB of dynamic range. Simple enough. With DSD you have one bit, so in a sense you have 6 dB of S/N, correct? But after noise shaping you have a S/N ratio of 120 dB? The step (leap?) that goes from 6 to 120 is where I’m not sure I understand. Does the 1 bit (6 dB) “snapshot” of DSD constantly move with the signal (music)? Given that single rate DSD samples at 2.8 MHz (double rate twice that), then the “snapshot” is capable of keeping up with the rapidly changing music signal, i.e., the sample is such a small sliver it will have far less than 6 dB of dynamic range? Assuming all that’s correct, this is fascinating and to me an elegant “do more with less” solution. Of course it’s the sound that matters, not the elegance of how you got there, and with DS we’ve already been through that…

#5

As a 1-bit format, DSD does have only 6.02dB of dynamic range. But this limited dynamic range is broadband across the entire frequency range below the Nyquist frequency (1.4112 mHz for DSD as it has a sampling rate of 2.8224 mHz).

DSD DACs use noise shaping to push this noise to over 20kHz. This results in a S/N of 120dB in the audible frequency range. And, of course, greater noise in the higher frequencies.

Another tidbit is that DSD cannot use dither, there is not room to do so when you only have 1-bit to work with. This is one of the reasons almost all modern DACs are between four and six bit. This allows for the least significant bit to be modulated with dither.

#6

Howdy

Noise shaping is simple at the 30,000 ft view:

Think of the rectangle defined by bandwidth (1/2 of the sample rate for PCM) and the S/N (approx. bit width * 6 for PCM). That box has a certain “area”.

When you use noise shaping you shift some of the area from the higher frequencies that you don’t care about on to the lower frequencies that you do.

For example you can (roughly) take the top 1/2 of the frequency and trade it for increasing the resolution. You can do that over and over.

Another way of looking at things is that a sigma delta A/D can be thought of as comparing a low pass filtered version of the digital output signal (e.g. what a sigma delta DAC does) to the incoming signal. If it’s too high a zero is output, if it’s too low a one is output. When the DAC in the A/D (and the DAC in your playback system) get a one they head for the positive rail as fast as the output filter allows, when they get a zero they head for the negative rail as fast as the output filter allows. The bandwidth of this process is set by that filter. But really it’s the high frequency component of the input and the noise from the single bit DAC that’s filtered away. By nuking the high frequency noise the A/D is only paying attention to the part of the signal we care about, the lower frequencies. The ones and zeros are trying to track the low frequencies and ignoring the high frequencies so you’ve traded off low frequency accuracy for getting gobs of noise in the high frequencies.

J.J. Johnson has a good slide deck out there somewhere. I’ll see if I can find it.

-Ted

#7

I enjoy the image of blowing the high frequency noise into bit history.

#8

Oh my, I think my brain has gone in for spring cleaning (have been in a bit of a fog lately, must be the long winter). Not totally comprehending what Ted and Elk said. Let me stew over the information for a day or two and if any visual aids are available that might help too.

#9

Think of it as having a bunch of dust on the floor of a room. It is a big room and your guests will only be in the entry. To make the room appear clean, you brush all of the dust to the back of the room.

The total amount of dust is the same, but you have moved it away from the area of the room you want to be clean. This is the same concept.

My guess is what is bothering you is the lack of an explanation of how noise shifting is actually accomplished on a 1-bit signal. The math gets a bit complicated. This is where Ted works his magic.

Basically, the noise in the audible frequencies gets filtered out as an error signal. This error is then subtracted from the input, leaving us with less noise in the audible frequencies. The filter is designed so that it tidies up the frequencies we care about, but allows lots of noise in the higher frequencies.

It is sort of like a dust broom that works on only the front entry, but then dumps the dust at the back of the room.

I hope this does not confuse you more.

#10

The total amount of dust is the same, but you have moved it away from the area of the room you want to be clean.

Thanks for making me realize that I have been doing DSD for almost whole my life :D

#11

Thanks for making me realize that I have been doing DSD for almost whole my life :D

:D

#12

When I’ve tried DSD, it sounded great except there was something that bothered me. It wasn’t something I could hear directly, but was a kind of “pressure” in my ears that over extended listening was unpleasant. Now, I don’t know what it was that I experienced, but my suspicion was that it was related to that “pile of noise” that got pushed into the high frequencies. Yes, I know that noise at those frequencies should be inaudible to humans. Note that I said it wasn’t that I “heard” ultrasonic noise, but that I “felt” something that was just not right.

My question re the DirectStream DAC is where (i.e. to what frequencies) does the DSD noise get dumped? Given that the final DSD data stream is running at 10x DSD, I’m hoping that the answer is that it is pushed to some frequency range far enough above 20k Hz to be totally removed by subsequent conversion to 2x DSD and low pass filtering.

#13

Tho the noise gets shifted to higher frequencies the output filter should tame it down quickly.

Some modified players might not filter the highs as much as they should, but by spec the ultrasonic noise on an SACD player shouldn’t rise above -40dBFS. This is 1/100 of full scale. Many (most?) players filter more out and as the frequency rises the noise drops off quickly.
Anyway here’s a plot with my noisy scope of the noise floor of the DirectStream. The noise floor and the spikes are from the scope not the DirectStream. Still you can clearly see the DSD bump and you can see that it’s not too big and that the output filter is starting to bringing it back down. That’s one reason I upsample to double rate DSD.

I have definitely felt the pressure you mention, in one system it was from the Nordost Valhalla cables. I don’t know what they did to the ultrasonics but they sucked in at least that system.

#14

Thanks Ted for your reply. I was especially glad to read that you’ve also experienced the anomaly I mentioned. In the graph you posted, are the values of the x-axis in kilohertz?

#15

Yes. And an impressive noise floor.

#16

Great explanation. It;s quite funny that there always seems to be a fight going on in the audiophile world. Mono vs. Stereo, tube vs. solid state, dolby vs. no noise reduction (or DBX), ABX testing vs. not, objective vs. subjective, vinyl vs. CD, balanced vs. single ended, and now we have DSD vs. PCM. I love a good dog fight!

#17

@Ted,

So what you are saying is that any aliasing (by transition of the shaped noise into the audible area during the LP filtering) is not a probable outcome (or significant worry for that matter), if done right?

#18

Ted, what happens to the noise and the listening experience when you play the Directstream through a system with super tweeters installed?

Esau

#19
@Ted,
So what you are saying is that any aliasing (by transition of the shaped noise into the audible area during the LP filtering) is not a probable outcome (or significant worry for that matter), if done right?

The purpose of shaping noise is exactly to keep the level of any noise proper to a low enough level to not be a problem. What you can't see in my plot because of the scope's floor is that the noise is well below what you see in the plot (continue the line down to the left from what it looks like at 57k to get an idea of how low it is in the digital signal.)

Aliasing can happen when you change sample rates up and haven't bandlimited your input to 1/2 the sampling frequency. In this case I filter out everything over 1/2 of 2 * 64 *44100kHz before upsampling to 10 * 64 * 44100kHz and then back to 2 * 64 * 44100 so there's no aliasing.

They are two independent things.

#20
Ted, what happens to the noise and the listening experience when you play the Directstream through a system with super tweeters installed?

Well I have the JMLab Nova Utopia Beryllium speakers whose linear tweeter respond well past 40k. (And the rest or my system well past 100k.)

As you see in the plots the noise is completely insignificant (-90dB) compared to the high frequency material that should be in a 192kHz recording.