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Copyright 2012 by Wayne Stegall
Updated April 20, 2012.  See Document History at end for details.




Digital Audio Formats


Introduction

Sony discontinued its last SACD player recently.  I thought it well to revisit the different digital audio formats: why they are different and why high resolution formats are better than the 44.1kHz/16bit format of CD.

Density Modulation

Analog digital systems require signal formats that originate and look digital but which yield their underlying analog signal simply by lowpass filtering.  These signals are linear because a linear filter can recover the original signal from the composite signal containing an error signal creating the sharp digital edges.

Where f(t) is the analog signal and e(t) the modulated quantization noise
f(t) + e(t)
 Analog LPF 
f(t)



pam
 Analog LPF 
sine
PAM is simply the time sampled analog signal produced by sampling the analog signal on the sampling clock transition and holding that value until the next clock transistion loads the next sample.  This format has the significant advantage of already closely resembling the analog signal before filtering.

pam
 Analog LPF 
sine
In PWM the width of each pulse is proportional to the analog signal level.

pam
Analog  LPF 
sine
A clever circuit known as a delta-sigma modulator produces a stream of synchronized pulses the average of which represents the input signal with unexpectly high resolution.  This bitstream format has a downside.  Because signal energy cannot be fully represented by any single 0 or 1 pulse, the remainder of unspent sound energy is always passed to the next sample to complete processing.  This smears the signal across pulses in a manner that is effectively random high-level jitter.  Estimating that the energy smeared to the next pulse is half of that spent or less, peak modulation jitter would be expected to approximately half a DSD sampling period.  Fortunately DSD operates at much higher clock speeds than does PCM.  Single rate DSD operating at 64x oversampling at 2.8224MHz would calculate 177.154ns jitter on this presumption.  On first thought, this large amount of jitter would be expected to have a bad effect on the sound, but instead is mitigated greatly by some virtue, likely its randomness.  Consider that smaller amounts of jitter of different character adversely affect the sound of DACs having a DSD stream in any form.  It is likely then that delta-sigma induced jitter effect is benign, its only effect to subjectively soften the impact of high-frequency transients, an effect that some consider euphonic.

pamdsd
Analog  LPF 
sine
Multilevel delta-sigma DACs output a composite density modulation signal comprised of high-level PAM modulation added to low-level DSD modulation.

Definitions

Definition of terms or abbreviations used.


The Original Format

The following is the original analog digital signal chain when compact discs were first introduced.

Ideal PAM PCM Digital Audio Chain


PCM ADC



PCM DAC


signal
Analog LPF
analog


S/H
PAM


SA
ADC
PCM



PCM


R2R
DAC
PAM


Analog LPF
restored signal

The sound of the chain was considered at the time to be inferior to analog due to the poor audio quality of the high order elliptical anti-imaging filter deemed necessary at the end of the chain.  Now audiophiles have found excellent reproduction from this chain if the elliptical lowpass filter is omitted. 


Oversampling

Oversampling the digital audio chain was devised to ease the analog filter requirements.

Ideal Oversampled PAM PCM Digital Audio Chain


PCM ADC



PCM DAC


signal
Analog LPF analog


S/H
PAM


SA
ADC
PCM


Downsampling
Digital Filter
PCM



PCM


Upsampling
Digital Filter
PCM


R2R
DAC
PAM


Analog LPF
restored signal

By sampling the audio signal some multiple higher than the stored sample rate then restoring the higher sample rate before conversion back to analog, the interval between the highest audio frequency and the highest frequency supported by the oversampled sample rate gives room for adequate lowpass filtering with more gentle and more musical analog filters.

On second thought I realized that the successive-approximation ADC would have become technologically unfeasable to use with oversampling at this point in development because it operates a number of bits times faster clock rate than its equivalent DAC.  In an 8x oversampled 44.1kHz/16bit system its feedback loop would operate at 5.6448MHz.  This difficultly was met then with the development of the analog ΔΣ modulator.  The previous chart the represents an ideal that met a technological roadblock and also my fantasy of what an ideal full PAM high resolution chain would consist of.  Here is the more practical oversampled signal chain.



ΔΣ ADC



PCM DAC


signal
Analog LPF analog


Analog
ΔΣ Modulator 
DSD


Decimation Filter
PCM



PCM


Upsampling
Digital Filter
PCM


R2R
DAC
PAM


Analog LPF
restored signal


Graph illustrating how oversampling improves analog filter application at 44.1kHz sampling rate.
antialiaslpfcmp
Legend:
Magenta:  Harsh eighth-order filter barely meets 22.05kHz anti-aliasing limit without oversampling.  (Here a Chebychev plot is substituted for a similar appearing elliptical one.)
Cyan:  Musical third-order Bessel filter performs better against 176.4kHz anti-aliasing limit with 8x oversampling.


A New Idea

Because the R2R resistor ladders in early DACs were expensive to trim for low distortion, the invention of the one-bit delta-sigma modulator promised to reduced the overall cost of converters by creating a conversion process whose accuracy relied only on the accuracy of its time base and not on component tolerances.

One-bit Delta-Sigma PCM chain


ΔΣ ADC



ΔΣ DAC

signal
Analog LPF analog


Analog
ΔΣ Modulator 
DSD


Decimation Filter
PCM



PCM


Upsampling
Digital Filter
PCM


Digital
ΔΣ Modulator
DSD


Analog LPF
restored signal


A Mixture of New and Old

Because one-bit digital was thought to lack some of the virtues of PAM, DACs were developed which produced a composite output consisting of PAM for high level changes plus DSD to fill in the low level detail.  These were named Multilevel Delta-Sigma DACs.  The ADC end remained one-bit however.

Multi-level Delta-Sigma PCM chain


ΔΣ ADC



ΔΣ DAC

signal
Analog LPF analog


Analog
ΔΣ Modulator 
DSD


Decimation Filter
PCM



PCM


Upsampling
Digital Filter
PCM


Multilevel Digital
ΔΣ Modulator
PAM + DSD


Analog LPF
restored signal


Eureka!

Digital audio conversions by some date became dominated by delta-sigma converters.  However, conversions between PCM and DSD are lossy.  If PCM is removed from the One-bit Delta-Sigma PCM chain and the signal is transmitted as DSD a very simple signal path emerges.  The DSD stream only needs an analog LPF to retrieve the signal from the digital hash.  Because the 64x DSD stream used for CD resolution converters has always had a equivalent 20-bit resolution, the simple DSD chain gains high resolution status as well.  This is the idea behind SACD.

Ideal DSD chain
signal
Analog LPF analog


Analog
ΔΣ Modulator 
DSD



DSD


Analog LPF
restored signal

Practical Problems

Debates over which of SACD or DVD-A is better favors DVD-A in the context of PAM converters.  The dominance of delta-sigma converters lends favor to the simple DSD chain.  However when editing is necessary the PCM and DSD both have nearly the same signal chain.  Only the storage of the signal occurs at a different point and a different format.  This is because DSD signal must be converted to PCM for editing.

Edited Delta-Sigma PCM chain (DVD-A)


ΔΣ ADC





ΔΣ DAC

signal
Analog LPF analog


Analog
ΔΣ Modulator 
DSD


Decimation Filter
PCM


Digital
Editing
PCM



PCM


Upsampling
Digital Filter
PCM
Multilevel Digital
ΔΣ Modulator
PAM + DSD
Analog LPF
restored signal

Edited DSD chain (SACD)


ΔΣ ADC



Partial ΔΣ DAC





signal
Analog LPF analog


Analog
ΔΣ Modulator 
DSD


Decimation Filter
PCM


Digital
Editing
PCM


Upsampling
Digital Filter
PCM
Digital
ΔΣ Modulator
DSD
DSD
Analog LPF
restored signal


Conclusions

All agree that both high-resolution PCM and DSD signal chains improve over the 44.1kHz/16bit CD format.1  From there opinions diverge.  PCM has an obvious advantage of more closely resembling the analog signal before low pass filtering, an advantage attributed to greater transient sharpness.  DSD has a certain softness created by the noise shaping process that makes it a euphonic preference for some.  As already stated, adding editing to the process makes the two signal chains similar.  Then the following are the only other considerations.  The high resolution PCM signal chain could finish its chain with added transient sharpness if PAM or the common Multilevel Digital ΔΣ DAC's are used.  Alternatively the PCM to DSD conversion near the end of the DSD signal path can be and is likely processed with optimal algorithms offline from the real-time limitations that limit the same part of the ΔΣ PCM chain.  In the end, choosing a format is a matter of preference.



1See article Mathematical Consideration of Some of the Limitations of Digital Audio for a discussion of CD format limitations.

Document History
April 18, 2012  Created.
April 18, 2012  Made minor corrections and added a little extra text.
April 19, 2012  Added graph illustrating how oversampling improves analog filter application.
April 20, 2012  Added extra material correcting presumptions contrary to the limitations of the successive-approximation ADC.