Digital audio effects applied directly on a DSD bitstream

Abstract

Digital audio effects are typically implemented on 16 or 24 bit signals sam-pled at 44.1 kHz. Yet high quality audio is often encoded in a one-bit, highly oversampled format, such as DSD. Processing of a bitstream, and the application of audio effects on a bitstream, requires special care and modification of existing methods. However, it has strong advantages due to the high quality phase infor-mation and the elimination of multiple decimators and interpolators in the re-cording and playback process. We present several methods by which audio effects can be applied directly on a bi tstream. We also discuss the modifications that need to be made to existing met hods for them to be properly applied to DSD audio. Methods are presented through the use of block diagrams, and results are reported.

Full text

Proc. of the 7th Int. Conference on Digital Audio Effects (DAFX-04), Naples, Italy, October 5-8, 2004
DAFX-1
DIGITAL AUDIO EFFECTS APPLIED DIRECTLY ON A DSD BITSTREAM
Josh Reiss and Mark Sandler
Centre for Digital Music
Queen Mary, University of London
Mile End Road, London E14NS, U.K.
josh.reiss,mark.sandler@elec.qmul.ac.uk
ABSTRACT
Digital audio effects are typically implemented on 16 or 24 bit signals sam-
pled at 44.1 kHz. Yet high quality audio is often encoded in a one-bit, highly
oversampled format, such as DSD. Processing of a bitstream, and the application
of audio effects on a bitstream, requires special care and modification of existing
methods. However, it has strong advantages due to the high quality phase infor-
mation and the elimination of multiple decimators and interpolators in the re-
cording and playback process. We present several methods by which audio effects
can be applied directly on a bitstream. We also discuss the modifications that
need to be made to existing met hods for them to be properly applied to DSD
audio. Methods are presented through the use of block diagrams, and results are
reported.
Keywords: Sigma Delta Modulation, SACD, DSD, Digital Audio Effects,
Bitstream Signal Processing
1.
INTRODUCTION
One-bit signals are used throughout the audio recording, editing and playback
process. Most analog to digital and digital to analog converters employ a sigma
delta modulator that converts a signal to a bitstream. Digital audio is often stored
during production in a single bit format. In addition, the high-end audio distribu-
tion format, SuperAudio CD, employs the single bit recording format known as
Direct Stream Digital, or DSD.
The benefits of the DSD format are numerous. Improvements in the traditional
pulse code modulation (PCM) format from higher bit rates and higher sampling
rates have experienced diminishing returns. This is partly due to the difficulties
in implementing accurate high bit quantisers, but primarily due to the losses
incurred from filtering. PCM systems require steep filters at the input to block
any signal at or above half the sampling frequency. Ideally, a brick wall filter
should be used; passing all frequencies below the Nyquist frequency, and reject-
ing all above. Yet an ideal brick wall filter does not exist.
In addition, requantization noise is added by the multi-stage or cascaded decima-
tion (downsampling) digital filters used in recording and the multi-stage interpo-
lation (oversampling) digital filters used in playback. Increasing the sample rate,
as with DVD-Audio, eases the difficulty of the brick wall filter, but does not
correct the problems introduced by multi-stage decimation and interpolation.
1 bit ADC
Front End Decim-
ation
Filter
PCM
Recorder
Interpol-
ation
Digital
Filter
SDM Analog
Low-pass
Filter
PCM
1 bitADC
Front End DSD
Recorder Analog
Low-pass
Filter
DSD
Figure 1:
The
s
tandard multibit PCM recording amd playback chain, (a), re-
quires a decimation filter on the recording side and an oversampling filter on
the playback side, whereas Direct Stream Digital, (b), enables sound to be re-
corded directly in the 1-bit signal format and eliminates the need for thes e fil-
ters.
This was the inspiration for a 1 bit audio format, as first proposed by Angus[1],
and independently implemented as Direct Stream Digital (see Figure 1). As in
conventional PCM systems, the analog signal is first converted to digital by 64x
oversampling sigma delta modulation. The result is a 1-bit digital representation
of the audio signal. Where conventional systems immediately decimate the 1-bit
signal into a multibit PCM code, Direct Stream Digital records the 1 -bit pulses
directly.
The resulting pulse train has some remarkable properties. The bandwidth now
extends over more than 1.4MHz. Through the use of high order sigma delta
modulators (SDMs), the noise can be shifted up to inaudible frequencies. And the
digital-to-analog conversion is now as simple as running the pulse train through
an analog low-pass filter.
Ultra-high signal-to-noise ratios as required for DSD in the audio band are
achieved through 5th-order noise shaping filters. Thus DSD can represent signals
with a frequency response from DC to 100 kHz. The residual noise power is held
at -120 dB through the audio band.[2]
Although single bit, oversampled formats have been found to be excellent for
archiving, A/D and D/A conversion, and recording[3], they suffer from a serious
drawback in the editing and mastering phase. Few tools have been developed
which allow effective processing of audio bitstreams. To apply audio effects
directly on the bitstream, it is vital that requantisation, decimation and interpola-
tion be kept to a minimum.
However, processing and audio effect creation in the 1 bit domain is appealing for
many reasons. The oversampled signal has very high quality phase information,
making phase vocoder-based effects easier and more accurate. Effects using vari-
able delays, such as chorus and flange, also benefit from oversampling since
interpolation of the delay is far more precise. Furthermore, 1-bit audio effects can

Proc. of the 7th Int. Conference on Digital Audio Effects (DAFX-04), Naples, Italy, October 5-8, 2004
DAFX-2
be applied on the DSD signal directly before or after encoding, thus maintaining
the simplified production chain as in Figure 1.
The goal of this paper is to describe how to develop standard audio effects on the
DSD bitstream, while minimizing intermediate conversions to multibit format
(thus destroying all benefits of DSD). Previous work[4-12] has already estab-
lished that suitable IIR and FIR filters can be created, as well as some mixing
tools. However, common audio effects, such as compandors, expandors, reverb,
modulation, and so on, have not yet been developed. In the following sections we
will demonstrate how these effects can be applied directly on a bitstream without
introducing unwanted artifacts, or significant degradation of audio quality.
2.
PROPERTIES OF THE DSD BITSTREAM
There are several features of DSD which distinguish it from PCM. At its heart,
DSD is specified as being a 1-bit format, with a sampling rate of 64*44.1kHz, or
2.8224MHz[13]. Little else is specified regarding the format, although co n-
straints are imposed for the archiving of DSD on SuperAudioCDs and the play-
back of those CDs (notably, restrictions on noise levels, frequency response, peak
levels and DC offsets). However, the specifications of DSD also note the follow-
ing properties
1.
The 1-bit format is such that the 1 represents a positive output (+1) and the 0
a negative output (-1).
2.
The 0 dB reference level has been set to 50% of the maximum theoretically
possible modulation depth. Atleast 4 out of any 28 consecutive bits must be
set to 1 (and similarly for 0). This maximum setting corresponds to 3.10dB.
3.
Silence patterns are defined as repeating bytes where each byte contains an
equal number of 1s and 0s.
Unlike PCM, the DSD signal always has a power of 1 (the bits representing +1
and -1 levels). Thus any instantaneous measurement of signal level is meaning-
less. Furthermore, whereas PCM has a strict 0dB maximum, the 0 dB limit for
DSD has been imposed as a safety measure. In practice, this means that a DSD
signal, when put through a sigma delta modulator, is unlikely to result in insta-
bility or severe clipping since its peak levels have already been restricted to
within safe margins.
Silence patterns do not make sense in 44.1kHz PCM since any repeating pattern
would be =22.05 kHz and hence potentially audible. A constant DC level repre-
sents silence in PCM. But for a DSD signal, constant levels (i.e., all zeroes or all
ones) are not allowed. A repeating pattern of 8 bits or less, on the other hand, only
has frequency components above 176kHz, i.e., far outside the range of human
hearing. Thus whenever inaudible output is required, a silence pattern should be
used. This is important in the construction of many audio effects, such as noise-
gating.
3.
TIME-DOMAIN AUDIO EFFECTS
Most time-domain based audio effects have well -established implementa-
tions[14]. The general design of these effects, when implemented on a DSD
signal, can follow the design used for PCM signals. In this section we describe
those design modifications which are necessary for DSD.
3.1.
Bitstream addition
Perhaps the most fundamental signal processing is the addition of two signals.
O’Leary and Maloberti[15] demonstrated an elegant bitstream adder (Figure 2).
The oversampled nature of the bitstream allows one to use a simple feedback loop
whereby two bitstreams are added along with the sum bit from the previous
iteration. When the bandwidth of the input signals is far below the sampling
frequency, as is the case with DSD, the output carry bits are an excellent represen-
tation of the average of the two signals.
This bitstream adder is remarkable because it requires no requantisation, and it
has been shown to be highly effective for oversampled signals.
The alternative,
bitstream addition via the interleaving of bitstreams[16], suffers degradation of
audio quality due to downsampling, phase shift and possible introduction of
low-frequency noise.
However, although this bitstream adder does not explicitly perform requantisa-
tion, it amounts to the same effect. Thus it acts as a first order sigma delta modu-
lator and introduces some noise and distortion into the audible band. The bit-
stream adder is suitable either for a limited duration, or when increased noise is
acceptable. An alternative would involve summing the signals and then perform-
ing high order noise shaping.
+
z
-1
sum
carry
A
BA+B
2
Figure 2:
A bitstream adder.
3.2.
Delay based effects
By using the bitstream adder in conjunction with multiple delays, it is possible
to create a flanger or chorus effect entirely through simple logic operations on the
bitstream. This is indicated in Figure 3, where BSA represents the bitstream
adder from Figure 2.
This implementation is very elegant and appealing because it requires no filter-
ing, decimation, interpolation or requantisation. It deals solely with bit opera-
tions and delays. Furthermore, the delays can be set to any length, and due to the
high sampling rate of DSD, there are far more options over the number of voices
and their placement. To weight the delayed signals, a given delay time may be
repeated in the inputs to the bitstream adders.
DSD
Input z
-n
1
z
-n
2
...
z
-n
3
BSA
BSA
z
-n
k-1
z
-n
k
BSA
BSA
BSA
...
BSA
DSD
Output
Figure 3:
Implementation of a basic flanger or chorus using the bit-
stream adder (BSA) of
Figure 2
.

Proc. of the 7th Int. Conference on Digital Audio Effects (DAFX-04), Naples, Italy, October 5-8, 2004
DAFX-3
However, it suffers serious limitations in that it allows for no mixing of signals
other than additively. Furthermore, the number of signals mixed in this way must
be a power of 2. Successive use of the bitstream adder in parallel and series may
mimic the effect of a multiplier, but significant noise might then accumulate in
the audio band, and it still does not allow for easy implementation of a gain
control. A bit stream multiplier is essential for volume adjustment, or for versa-
tile mixing of signals. Therefore, most effects will be implemented using conver-
sion to a multibit domain, and then a sigma delta modulator in the final stage is
used for requantisation to DSD. As shown in Section 4, this SDM can sometimes
be incorporated into the effect processing stage.
3.3.
Level detector
In order to implement many effects, such as noise gating, expansion, limiting and
compression, a level detector is required. In PCM, this is trivial, since the instan-
taneous level is given by the quantised signal at any given time. For a bitstream,
however, the instantaneous value is either 0 or 1, corresponding to a 1 or -1, for
input over the range[-Max, Max] where the maximum absolute value of the input
is some value Max<1.
Nevertheless, PCM level detection usually employs a time average d power of the
signal and bitstream level detection can do the same. It is important however, that
the time average be over roughly the same amount of time but not over the same
amount of samples. The high oversampling rate demands this.
Time average level detection becomes even simpler for DSD signals. RMS esti-
mation of power is unnecessary. One can simply count the bits. Over a window of
size N, where M is the number of ones in the window, P=|N -2M|/N gives an
estimate of the power. A value between 0 and 1 for P can set the threshold. For
most dynamic processing, standard techniques can then be applied. A variable
gain can multiply the signal, with the additional requirement that the output is
processed through a sigma delta modulator (and optionally, a low pass filter), to
return the signal to DSD format.
For an accurate envelope detector, a simple moving average filter should not be
used. A decimation filter is preferred since it more accurately represents the mul-
tibit level of the signal at any instance. It is important to note that under such a
situation, decimation need only be used for level detection, and no additional
decimation/interpolation is applied to the bitstream.
3.4.
Modulators
Modulation involves the multiplication of an audio signal by some carrier signal,
typically a sinusoid. To do this using entirely DSD signals would involve the
multiplication of two bitstreams. Unfortunately, this is not as simple as the
addition of bitstreams as in Figure 2. The product of two single-bit signals can be
obtained with just one logical gate, an XNOR (or an AND if the signals were
restricted to [0;Max]). However, this approach affects the noise-shaping character-
istics. Multiplication in time domain corresponds to convolution in z-domain.
Therefore, the resulting bit-stream has four components: one from the convolu-
tion of the two signals, two from convolutions between one signal and the shaped
noise of the other bitstream, and the last from the convolution of the two shaped
noises. Since the last term has a flat frequency spectrum, the result of a multipli-
cation of two noise-shaped bitstreams is a non noise-shaped waveform, whose in-
band noise limits the accuracy of processing.
DSD
Bitstream
X
SDM
DSD
Output
Figure 4: M
odulation of a DSD bitstream.
Currently, the only alternative is to perform multiplication of DSD signals via
decimation to a multibit domain, and then reconverting to DSD via upsampling
and requantisation. This suffers severe drawbacks because of the introduction of
low frequency noise.
However, since, the carrier signal is intended to be an internally generated wave-
form, it need not be in DSD format. This allows for mixed domain processing.
The carrier signal can be generated multibit, at the DSD sampling rate. The DSD
bitstream can then be multiplied by this multibit signal, and converted back to
single bit output. Filtering of the output should be kept minimal since the pur-
pose of most modulators, such as ring modulation, is to introduce new frequen-
cies. This system is depicted in Figure 4.
3.5.
Noise gating
An extreme noise gate operates simply as a threshold below which there should
be no signal. A noise gate operating on a DSD signal has several important dis-
tinguishing characteristics which require modifications of the standard PCM
noise gate in order to function. First, the level detector or envelope follower
requires modification, as mentioned in Section 3.3.
Noise gating however, requires further modification. When the signal has been
faded to zero, the output must correspond to DSD silence. It is conceivably pos-
sible that traditional techniques will produce a signal that, although representing
the output of an SDM acting on zero input, will not be silent[17, 18]. This could
occur due to small DC offsets or initial conditions of the SDM. This problem is
especially serious because, rather than this signal being a very high frequency
pattern, as DSD silence is defined, it may be a very low frequency patt ern and
hence audible.
For these reasons, when silence is required at the output, as may be the case in a
noise gate, the output bitstream is replaced with a DSD silence pattern. If smooth
transitioning between silence and low-level signal is required, then one of the
switching techniques described in Section 3.6 can be applied during the fade-in
and fade-out stages.
3.6.
Smooth mixing and switching of bitstreams
It is well-known that switching of PCM signals can result in audible artefacts due
to discontinuities in the output signal. This is avoided by strictly requiring that
the PCM samples from the initial and replacement streams be identical at the
point at which the switch is made. Samples around the switch should also be
roughly identical to prevent abrupt changes in signal slope (and instantaneous
frequency) as well.
But the DSD signal contains historical information. That is, the current signal is
determined by a sequence of bits, and the next bit is a function of prior states as
well as current input. Thus, sample matching is not sufficient. Smooth switching
requires that the switch happen when the two bitstreams are synchronised.

Proc. of the 7th Int. Conference on Digital Audio Effects (DAFX-04), Naples, Italy, October 5-8, 2004
DAFX-4
DSD
Silence
Level
Detector
DSD
Bitstream
Figure 5:
A hard noise gate implemented on a DSD bitstream. A DSD
silence signal must be used since constant DC levels are not possible.
In [19], Reefman and Nuitjen described an approach to synchronisation of bit-
streams which allows for seamless switching. This approach involves the use of a
sigma delta modulator acting on the mix of the two input bitstreams. However,
this SDM must be synchronised such that it produces the bitstream A when
acting just on A, and the bitstream B when acting just on B.
In order to produce synchronisation, the integrator states, or initial conditions of
the SDM, must match those integrator states. This synchroniser can be imple-
mented by using a least squares approach to find integrator states which mini-
mise the difference between a DSD input signal and the resulting DSD output
signal. Thus editing is done as depicted in Figure 6. When synchronisation is
ready, the switch is changed to the central position, and G is set to 1. G is slowly
decreased to 0, then the output stream is resynchronised to input stream B, and
the switch is set to the downwards position.
An alternative switching method is proposed in Figure 7. We note first that both
input and output streams are low-pass filtered, and the application of a slowly
changing gain and a first order SDM should not significantly change the band-
width of the signal. Importantly, a first order SDM will have no effect on a DSD
bitstream. The difference between quantization of a bit and the original bit is zero.
Thus, when G is set to 1 in Figure 7, the output bitstream is A. As G is decreased,
a cumulative error based on the difference between the 2 input signals is added to
the quantiser input. As G approaches 0, the difference between the output and
input bitstream B also approaches 0. Eventually, the feedback term approaches a
constant (typically non-zero) and the output bitstream is identical to B. The only
significant introduction of noise is the non-shaped noise due to the first order
SDM acting on the sum of two bitstreams when the gain is in the region
0<<G<<1. However, this occurs over a relatively short period and is minimized
since both inputs are already low-pass filtered.
A
B
G
1-G
+
SDM
z
-n
z
-n
Sync1
Sync2
Figure 6:
Smooth switching between bitstreams using synchronisation.
A
B
G
1-G
+
z
-1
Q
+
-
+
Figure 7:
Smooth switching between DSD bitstreams using a slowly
changing gain and a first order SDM.
The result of this switching scheme on input signals of frequency 1 and 2 kHz, is
depicted in Figure 8. A switch is desired at 2 milliseconds. The example is par-
ticularly pernicious (and somewhat unrealistic) since the waveforms are very
different; out-of-phase and with peak amplitudes of 0.2 and 0.9. The gain is
changed linearly from 1 to 0 over 1,600 samples, or just over half a millisecond.
Depicted are the analog input signals before conversion to bitstreams, and the
output signal after decimation to multibit, 44.1kHz using a sinc
2
filter. The re-
sulting transition at 2 msecs is smooth without abrupt changes in amplitude or
slope. There is a slight and temporary increase in frequency, but this effect can be
minimised through the use of a slower gain change or eliminated completely by
using a detection scheme to find a more appropriate time to perform the edit.
Improvements to this method could also be achieved by using a more effective
noise shaper (higher order SDM) instead of the first order SDM in Figure 7.
However, with gain equal to 1, the output bitstream would not be identical to the
input bitstream. To phase out the effects of requantisation, and resynchronize the
output bitstream with the input stream A, we can slowly redu ce the feedback
coefficients of the modulator. As feedback coefficients approach zero, the modula-
tor becomes lower order until it approaches a first order SDM, and as before, has
no effect on the bitstream.
-1.0
-0.5
0.0
0.5
1.0
Analog Input
43210
-1.0
-0.5
0.0
0.5
1.0
Decimated Output
43210 Time (msec)
Figure 8:
Smooth switching between DSD bitstreams using the cir-
cuit from
Figure 7
. This is the worst case scenario, where the input
bitstreams have differing amplitudes and opposing phases.

Proc. of the 7th Int. Conference on Digital Audio Effects (DAFX-04), Naples, Italy, October 5-8, 2004
DAFX-5
4.
FREQUENCY-DOMAIN EFFECTS
Virtually all frequency-domain based audio effects, such as equalisers, wah-wah,
and phasers, require the construction of FIR or IIR filters. A significant body of
research exists on 1-bit filters. A full discussion of 1-bit filter designs is beyond
the scope of this work. Here, we note the main research and how 1-bit designs
differ from their PCM-based equivalents.
Angus[4] provided a means of implementing FIR and IIR filters on the DSD
bitstream. This was based partly on prior work on FIR filters by Wong and
Gray[5, 6] and Kershaw, et. al.[7] and IIR filters by Johns and Lewis [8, 9], and on
his own work concerning the processing of one bit digital audio signals[10].
Equalisation is usually implemented by shelving filter design using first order
filters. In [4], Angus demonstrated a bass cut/boost co ntrol filter which acts
directly on the DSD bitstream. He reported roughly equivalent performance to
PCM equalizers.
4.1.
FIR Filters
Filters for DSD input and output signals have several design co nsiderations
which distinguish them from their PCM equivalents. The main alterations are
not the same for IIR filters and FIR filters[11]. For a one-bit FIR filter acting on a
64 times oversampled DSD signal, the delay line consists of
z
-
64
delays rather
than
z
-
1
delays. In effect, the taps are subsampled. This has the effect of zero-
interleaving the impulse response by a factor of 64. The fr equency response is
replicated throughout the entire frequency range. This would thus demand a high
order filter, except for the fact that this replicated response is outside the audible
range. In general, the out-of-band frequency response is irrel evant. Whether the
signal needs additional filtering is then dependent on the use of the filter and on
the requirements for the high frequency content of the signal. Alternatively, one
could redesign the filter using single delays and take into account the high sam-
ple rate and single bit input. This approach involves a combination of cascaded
integrators and a sparse tap filter[4]. It is efficient, removes the high frequency
noise and can achieve the desired frequency response.
4.2.
IIR Filters
IIR filtering of a DSD signal, on the other hand, does not change the delays but
changes the coefficients. The coefficients of the filter can be calculated in the same
way as for PCM, but the oversampling implies that their values will be very
different.
As has been mentioned, requantisations should be kept to a minimum. Thus, if
the filtering consists of IIR/FIR filters, a noise shaping filter and a low pass filter,
then these stages should be combined in such a way that there is only one requan-
tisation in the final stage. Figure 9 depicts an IIR filter which incorporates an
SDM-based requantiser. Although such a design is efficient and eliminates the
multi-bit stage, it does not differ greatly from a cascade of one bit filters followed
by a remodulator.
Minimising decimation, interpolation, and requantisation is not a drawback.
These filters add to system complexity and degrade pe rformance. In addition,
filtering in the oversampled domain is advantageous because it relaxes specifica-
tions on anti-alias and reconstruction filters at the analog interfaces, thus improv-
ing phase linearity[12].
Q
DSD
Input DSD
Output
z
-1
z
-1
z
-1
z
-1
z
-1
Figure 9:
Configuration of a combined IIR filter and remodulator.
5.
CONCLUSIONS
This work concerned how to apply audio effects directly on a DSD bitstream. The
general architecture of many effects is approximately the same. However, major
modifications need to be made to level detection, noise gating, and switching
methods. Conversions to the multibit domain, quantisations and filtering should
be minimized. Thus, wherever possible, processing stages should be combined
and a single requantisation step should be placed at the end.
One subject which has not yet been adequately investigated is an empirical com-
parison of audio effects implemented on PCM and DSD signals. All the effects
methods discussed within were analysed via the use of simple SDMs for requan-
tisation and a decimation filter allowing comparison with PCM effects. However,
this introduces further noise and thus direct comparison is not easy. Development
of sophisticated decimation filters and implementation of high order SDMs
would allow for a more rigorous analysis. Also, proper analysis of audio effects
on DSD signals requires listening tests comparing the signal before and after the
effect is applied. However, DSD signals are hard to come by. A new audio format,
DSDIFF, has been proposed for the exchange and storage of DSD-encoded au-
dio[20]. As the format gains acceptance, DSD sample files will become available
and direct comparison of audio effects on DSD and PCM signals will become
possible.
6.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the contribution of Prof. James Angus for his
comments and criticism concerning this work.
7.
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