PCM vs DSD. What is common base? [Article]

Audio Basis - educational articles

PCM and DSD are considered as different formats, as rule. But author think, that PCM and DSD are two side of a single phenomenon. Read below why.

Introduction, terms > From PCM to DSD > From DSD to PCM >

Sample rate issue > Conclusions > Read more about DSD >

DSD versus PCM. Common base

Video: DSD versus FLAC (PCM implementation)

Introduction, terms

DSD (sigma-delta modulation) is 1-bit audio format that use noise-shaping to increasing of dynamic range.

PCM (pulse code modulation) is multibit music format that use number bits to expanding of dynamic range.

Dynamic range is the difference between maximal and minimal allowable level of transmitted signal.

The maximal signal level cause overload.

Minimal signal level less than or equal to quantization noise level (a.k.a. noise floor). Signal "under" noise have bad recognizing.

Simplified dynamic range

Simplified dynamic range

Simplified dynamic range is difference between maximal level and noise floor.

Warning: It is not technically correct definition. But in frame of the article we will use it for easier understanding.

We can discuss dynamic range as common base for both PCM and DSD. Dynamic range is single matter for different bit depth.

Maximal level in the digital audio is accepted as 0 dB. It is not depend on bit depth. But noise floor depend on the bit resolution.

From PCM to DSD

As example, we have a certain noise level for some PCM bit depth.

After the bit resolution reducing, the noise level is higher and dynamic range is reduced.

Bit depth truncating (from PCM to DSD)

However noise level may be kept into limited useful frequency band. Noise energy, that grown due bit depth truncating, may be pushed out of the band via noise shaping.

Noise shaping, PCM to DSD transformation

It is very like to DSD. And, yes! It is real multibit DSD!

Read about PCM to DSD conversion and DSD to PCM converters here > and here >

From DSD to PCM

Now let me try to come from DSD to PCM. Here we also have given noise level.

Noise shaping may be characterized by the steepness. Both total and useful audio signal bands define the steepness.

Noise shaping steepness

Steeper noise shaping may be used to expand the useful band. So DSD 64 vs 128 (5.6 MHz) is matter of the steepness.

Higher steepness can cause lesser stabilty of sigma-delta modulator (noise shaper). So lesser steepness may be good.

Adding bit to sample word decrease noise level. So noise shaper's steepness may be decreased too. Because noise energy, that need to push out of the useful band, is lesser.

Adding bit - lesser the steepness, DSD to PCM transform

At last the noise floor become flat. So DSD signal is transformed to PCM.

Sample rate issue

DSD have significantly higher sample rate, than PCM, because band reserve is need to push excess noise energy out of the useful frequency band.

However, even simple band expanding cause lesser noise level. Because quantization noise energy is constant and distributed in full band. Graphically noise energy is square of the noise spectrum. It like to rectangle. If its width is expanded, height (noise level) diminish.

Sample rate and quantization noise level

Two times band expanding decrease noise level at 6 dB.

So we can say, that DSD decrease noise level twice:

by sample rate and
by noise shaping.

Conclusions

DSD and PCM are two side of one thing - transmitting of digital signal with given dynamic range.
To transform DSD to PCM need to increase number of bits and remove noise shaping.
To transform PCM to DSD need to diminish number bits with noise shaping and sample rate extension.
In author's opinion, most obvious DSD sign is partitial usage of total signal band to transmit signal and pushing noise energy out of the useful frequency band.

Yuri Korzunov, 2017