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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 - Pulse Amplitide Modulation

Analog LPF

• PWM - Pulse Width Modulation

Analog LPF

• DSD - Direct Stream Digital (AKA One-bit digital or Bitstream)

Analog  LPF

• PAM + DSD

Analog  LPF

Definitions

Definition of terms or abbreviations used.

• Decimation Filter -  A digital filter that downsamples and applies lowpass-filtering a one-bit stream to produce its PCM equivalent.
• Delta-Sigma (ΔΣ) Modulator - A circuit that produces a stream of synchronized pulses the average of which represents the input signal with unexpectly high resolution.  The analog version converts an analog signal to DSD and digital version converts PCM to DSD.
• Pulse Code Modulation (PCM) - the representation of a sampled analog signal by a sequence of numbers.
• R2R Ladder DAC - A DAC that transforms PCM to a PAM waveform by means of a resistor network having only two values of resistance R and 2R implemented by combined R valued resistors.  The PCM signal switches the input taps and the output represents the analog value of the code.
• Sample and Hold (S/H) - A circuit that creates a PAM waveform from an analog signal by switching the analog signal through a switch to a small capacitor at regular clock intervals.
• Successive approximation ADC (SA ADC) - An analog-to-digial converter that systematically guesses the correct PCM code for each sample of an analog signal presented sample by sample by a sample-and-hold front end.  The guess is feed back through and R2R DAC to be compared to the sampled analog signal.  The optimized method of guessing requires only one guess per bit before returning the best representative PCM code.

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.

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.