Z Systems rdq-6 User manual

rdq-6 instruction manual z-systems audio laboratories
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rdq-6instructionmanual
rdq-6 instruction manual....................................................................................................................................................1
introduction............................................................................................................................................................................1
physical layout.......................................................................................................................................................................3
•front panel controls................................................................................................................................................3
•rear panel layout .....................................................................................................................................................4
operational guide .................................................................................................................................................................5
•input selection.........................................................................................................................................................5
•stereo-linked/dual-mono mode.........................................................................................................................6
•output wordwidth (dither) selection................................................................................................................6
•volume control.........................................................................................................................................................7
•individual volume offsets.....................................................................................................................................8
•channel selection....................................................................................................................................................9
•bypass mode............................................................................................................................................................9
Transparent Tone Control.............................................................................................................................................11
•selecting filters.......................................................................................................................................................11
memory functions ..............................................................................................................................................................13
•save preset..............................................................................................................................................................13
•load preset..............................................................................................................................................................14
appendix A: equalization and dither.............................................................................................................................15
•equalization............................................................................................................................................................15
•dither........................................................................................................................................................................18
appendix B: the relationship between Q and slope................................................................................................22
appendix C: finite wordlength digital filtering..........................................................................................................23
appendix D: rdq-6 automation protocol ...................................................................................................................25
•Automation Port Reconfiguration ...................................................................................................................25
•Command Strings.................................................................................................................................................25
specifications........................................................................................................................................................................28
precautions...........................................................................................................................................................................29
warranty.................................................................................................................................................................................30
•other z-systems audio laboratories products...............................................................................................30
•contact information..............................................................................................................................................31
introduction
Congratulations on your purchase of the rdq-6 digital reference equalizer. The rdq-6 is the
result of many years of research and development in digital audio technology, and when used
properly, it will create a home theater experience you may not have thought possible from
your system.
The purpose of this document is to give you a complete understanding of the theory and
operation of the rdq-6 so that you may apply it properly in your home theater system. The
rdq-6 is a six channel digital tone and level control system that is used between an AC-3 or
DTS decoder and six channels of digital-to-analog conversion (realizable as either three
separate two-channel DACs or a single six-channel DAC such as our rdac-6). This is shown
schematically in Figure 1. The rdq-6 offers six bands of parametric equalization for each of six
discrete channels. The parametric equalization can be used for a wide array of purposes,

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including room correction, speaker matching, speaker compensation, or tonal shaping.
Additionally, the rdq-6 allows the user to control master volume, individual channel volume
offsets and dither all in the digital domain. With the rdq-6 in the signal path, there is no need
for an analog preamplifier; the DAC(s) can be connected directly to the power amplifier(s). In
this regard, it is useful to think of the rdq-6 as a digital domain preamplifier for your six-
channel home-theater playback.
The rdq-6 can also be used in a mode we call "super-two-channel mode" (S2 mode). When in
S2 mode, the rdq-6 can apply all of its equalization bands to a two-channel source, yielding
18 bands of parametric equalization per channel. This allows the rdq-6 to function much like
our rdp-1 and rdq-1 processors, but with more power and flexibility. For example, twelve of
the equalization bands could be used for room and speaker correction while the remaining
six are used as tone controls.
FIGURE 1
The rdq-6 also has a number of useful memory features that make it extremely versatile,
flexible, and easy to configure. The following pages will give you a simple “walking tour”
through the rdq-6. Appendices A, B, and C provide more detailed information.

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physicallayout
•front panel controls
Figure 2 shows the front panel in normal operating mode. Below, you will find a description
of all of the front panel controls on the rdq-6.
FIGURE 2
1. Display. 4 row by 40 character.
2. Signalvalidindicators. Separate LEDs indicate the presence of valid digital input signals
on the Left/Right Front, Left/Right Surround and the Center/Sub channels.
3. Bypass button. Pressing this button disengages all of the rdq-6's signal processing (with
the exception of the volume control) from the signal path.
4. Display dim/off. Pressing this button cycles the display through 5 different intensity
settings: 100%, 60%, 40%, 20%, and "off."
5. System menu button. Allows the user to access the input selection, load and save
functions, output wordwidth controls and the stereo/dual mono link controls.
6. Menu buttons. These multi-function buttons work in conjunction with the display. In
the normal operating mode shown above, pressing one of these buttons will bring the
filter shown directly above it "into focus." When in any other mode, the last row of the
display will show a menu bar. There will be six options on this menu bar, one per menu
button, across the bottom of the display. Pressing any of these buttons will execute the
corresponding function described by the word displayed directly above it on the menu
bar. All six buttons may or may not be active, depending on the mode. To aid in
understanding this, the illustrations in this manual will have the buttons "greyed out"
when they are not active in a particular mode of operation.

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7. Control knobs. The three large knobs on the front panel are used to change parameters
shown in the display. All three knobs may not always be active. To aid in understanding
this, the illustrations in this manual will have the knobs "greyed out" when they are not
active in a particular mode of operation.
8. Volume control button. Pressing this button puts the rdq-6 into a mode where either
the main volume or the individual channel volume offsets can be controlled.
9. Channel selection button. Pressing this button toggles the display and knobs between
the available channels. When a new channel is chosen, the display will show all of the
filter parameters for that channel.
10. Infra-redremotesensor.
•rear panel layout
The only audio connectors visible on the rdq-6's rear panel are three sets of XLR AES/EBU
digital inputs and outputs and three sets of RCA S/PDIF digital inputs and outputs. The main
power switch and the AC mains connector are also located on the rear panel. This is shown
in Figure 3.
FIGURE 3
1. Left/Right Front (Left/Right Room Eq 1) digital processor card.
2. Left/Right Surround (Left/Right Room Eq 2) digital processor card.
3. Center/Sub (Left/Right TTC) digital processor card.
4. S/PDIF digital outputs on RCA connectors.
5. AES/EBU digital outputs on XLR connectors.
6. S/PDIF digital inputs on RCA connectors.
7. AES/EBU digital inputs on XLR connectors.
8. Automation port.
9. AC power inlet module.
10. MAINS power switch.

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operationalguide
•input selection
The rdq-6 has three independent digital processor cards, Left/Right Front, Left/Right
Surround, and Center/Sub. Each of these cards has two digital inputs and two digital outputs.
The rdq-6 allows you to select which of the inputs is active through the input selection
function. There are a number of reasons why input source selection is best performed in the
digital domain. The most significant is the reduction of crosstalk. There is infinite rejection
between input channels on the rdq-6; crosstalk is simply not possible.
FIGURE 4
How to do it. Each digital processor card accommodates the digital audio input and output
for a stereo pair of channels. On each card, you will find 1 AES/EBU input on an XLR
connector, 1 S/PDIF input on an RCA connector, 1 AES/EBU output on an XLR connector, 1
S/PDIF output on an RCA connector. Regardless of which input is selected, both outputs are
active simultaneously. To select which input is used by the rdq-6, press the system button
and select the INPUT submenu. The display will appear as shown in Figure 4. To change the
active input, simply rotate the knob below the input selection display for each of the three
digital processor cards. To switch to S2 Mode, press the TO S2CH button. Doing this will
cause the screen to present a confirmation display. You should remember that the output of
the rdq-6 in S2 mode appears on the Center/Sub processor card outputs. When you have set
your DAC properly, hitting the CONTINUE button will complete the transition to S2 mode.
While in S2 mode, the board labels will change to L/R room eq 1, L/R room eq 2, and L/R TTC.
Pressing the button below BACK will take you to the system menu and pressing the button
below EXIT will take you to the normal operating mode.

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•stereo-linked/dual-mono mode
The Left/Right Front and Left/Right Surround digital processor cards can be configured to run
in either stereo-linked or dual-mono modes. In stereo-linked mode, the controls and displays
pertain to both the left and the right channels simultaneously. When changes are made to
any parameter, both channels will be affected. In dual-mono mode, you have independent
control of the left and right audio channels. The center/sub processor bank is always in dual-
mono mode.
FIGURE 5
How to do it. Press the system button and select the LINK submenu. The display will
appear as shown in Figure 5. To change the link mode, simply rotate the knob below the link-
mode selection display for the front and surround processor cards. If in S2 mode, the L/R TTC
label will also be shown and the link status for this board can be changed as well. Pressing
the button underneath BACK will take you to the system menu and pressing the button
underneath EXIT will return you to the normal operating mode.
•output wordwidth (dither) selection
For a more thorough discussion of dither, please refer to Appendix A.
The rdq-6 allows you to control the dither for each processor card so that each of the output
signals are compatible with your digital-to-analog converter(s). The rdq-6 carries out its
computations in 40-bit floating-point arithmetic, which then must be converted back to a
fixed-point representation usable by your DACs. Internally, the 40-bit result is first converted
to 24-bit fixed-point. The dither control then determines how many bits appear at the outputs
of the rdq-6 and how those bits are obtained. You can choose from:
•24 bits
•truncated to 20 bits (no dither)
•dithered to 20 bits
•truncated to 16 bits (no dither)
•dithered to 16 bits

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The rdq-6 allows you to set different output wordwidths and dither settings for each of its
three processor cards so that you can use different DACs for each channel pair. The majority
of DACs today use 20-bit digital-to-analog chips as their core conversion technology; hence,
we tend to recommend the 20-bit dithered output as the most useful across the broadest
spectrum of source material and DACs today. If you are using the rdq-6 with the z-systems
rdac-6, you can take advantage of the full 24-bit output. As 24-bit converters and 24-bit
digital filter chips become more commonplace, we will recommend the 24-bit output setting
for other devices.
FIGURE 6
Howtodoit. To select which dither mode is used by the rdq-6, press the system button and
select the WORD submenu. The display will appear as shown in Figure 6. To change which
dither mode is used, simply rotate the knob below the dither selection display for each of the
three processor cards. Pressing the button underneath BACK will take you to the system
menu and pressing the button underneath EXIT will take you to the normal operating mode.
•volume control
The analog volume control is a potential source for noise and coloration. Nonetheless, most
of us are willing to live with these problems in light of the other problems that life without a
volume control would cause! The rdq-6 features a digital-domain volume control and offset
facility which is utterly neutral tonally. This control allows you to apply between +12 dB of
boost and -95 dB of cut to the incoming digital signal and an offset between +12 dB of boost
and -95 dB of cut to every channel with respect to the left front channel. You may have heard
arguments that digital-domain volume control is undesirable because it leads to loss of
resolution. This may be true for poorly implemented digital volume controls but certainly is
not the case for the rdq-6. Remember the discussion of dither: we can achieve resolution well
below the least significant bit. This is the key to the rdq-6’s digital volume control (please
refer to appendix B for a more detailed explanation).

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FIGURE 7
How to do it. With the rdq-6 in normal operating mode, press the volume button. The
display will change as shown in Figure 7. To change the master volume, turn the center knob
until the desired value is shown on the display. You can also enter offsets relative to the left
front channel for the right front, left and right surround, center and sub channels. Please refer
to the next section for instructions on how to do this.
A special note about the rdq-6’s volume control. The rdq-6 always powers up to a default
master volume of –40 dB. Furthermore, volume is the only parameter not stored or recalled
by the load and save functions, nor is it affected by the bypass control. This is for an
important reason. Dangerous output levels could result when using the rdq-6 in a system
with no analog preamplifier. For example, suppose we designed the rdq-6 so that the bypass
control returned the volume to 0 dB. Hitting bypass during a loud passage would then result
in the system volume going to full-scale. The same could happen while comparing presets. It
is for this reason that the volume setting is unaffected by the load and save functions and
bypass; whatever the value of volume is dialed in will remain in place during preset loads or
during bypass.
•individual volume offsets
In a home theater system, it is not at all uncommon that the speakers may have markedly
different sensitivities from one another. Consequently, it is often necessary to be able to
control the relative levels of the signals going to each of the speakers. This is why we have
included a channel volume offset facility.
How to do it. If you are not yet in the volume screen, hit the volume button. Next, select a
channel for which to set an offset by pressing one of the buttons located directly underneath
FRONT, SURR and C/SUB to access the front, surround and center/sub offset screens. Figure 8
shows how the display will appear if the FRONT offset was chosen. Now, we have chosen the
Left Front channel as the offset reference. That is, all of the offsets will be relative to the Left
Front channel. Consequently, you will not be able to change the +00.0 dB shown for this
channel. Dial in an offset using the knob underneath the displayed offset you would like to
change.

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FIGURE 8
•channel selection
The rdq-6's display is only large enough to display the complete set of filter parameters for
one channel at a time. The purpose of the channel selection button is to scroll between the
filter parameters for each of the channels.
FIGURE 9
How to do it. With the rdq-6 in normal operating mode, press the channel button. Figure 9
shows how the display looks when we are displaying the the Left/Right Front channel
settings. To change which channel is being displayed, turn the center knob until the channel
you would like to see is shown. If either the front or surround processor cards are in stereo-
linked mode, you will not see the individual left and right channels for these banks; they will
be displayed as a stereo pair. The same is true for the TTC pair if it is linked mode. If you
would like to apply tone control separately to the left or right channels of either of these two
banks, please see the section entitled stereo-linked/dual-mono mode.
•bypass mode
Hitting the bypass button results in the state shown in Figure 10. The bypass modesets all of
the filters flat, cancels the dither and returns all of the volume offsets to 0 dB; only the master

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volume is left unchanged. When in bypass mode, none of the rdq-6’s controls are functional;
you must press bypass again to return to normal mode.
FIGURE 10
aspecialnoteonperformingA/Bcomparisons
The italicized text above makes it clear that the bypass control returns the output wordwidth
to 24 bits, canceling the dither that may have been selected. Perhaps most significantly,
however, the bypass mode does not affect the volume. This is because we want it to be
impossible for the user to accidentally bring the volume to full-scale. Because the bypass
mode cancels the dither, hitting bypass when the volume is set to anything other than 0 dB
can result in very subtle sonic differences due to truncation, depending on the program
material and the volume. Therefore, doing a level-matched comparison between a given EQ
setting and flat EQ using the bypass control is not really meaningful unless the volume is set
to 0 dB. A better approach is to set up a preset with all of the filters set flat and the dither set
as desired and use that preset in the A/B-compare mode.

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TransparentToneControl
For a thorough discussion of equalization, please refer to Appendix A. There, you will find a
complete explanation of concepts such as center frequency, bandwidth, gain, boost, bell
filters, and shelving filters. The reader who is familiar with these concepts may skip Appendix
A and proceed with the following.
Of all the rdq-6’s functions, the transparent tone control merits the most in-depth discussion.
Most high-end audio equipment does not include any form of tone control. There are several
reasons for this, but the simplest is that a tone control would require additional circuitry in the
signal path, which would lead to audible degradation of the audio signal. This reasoning is
indeed correct for tone controls, which work in the analog domain. The rdq-6, however,
works entirely in the digital domain. Z-Systems has developed a very sophisticated tone
control algorithm we call Transparent Tone Control (TTC) and the TTC facility built into the
rdq-6 is its most important feature. TTC is actually more than a tone control; it's a complete
digital-domain parametric equalizer that can be used subtly for speaker correction,
dramatically for room correction, or artistically, to sculpt the signal and make it sound the way
you want it to sound.
You may have a negative impression of digital-domain tone control; indeed, there have been
many poor implementations in the past. Rest assured: we're confident you'll find TTC to be
free from any non-beneficial coloration and to be the finest tone control you've ever heard.
TTC is a direct implementation of the digital equalization algorithm used in our line of
professional disc mastering equalizers. In fact, there's a good chance many of your compact
discs were prepared using one of our equalizers and that TTC was used in the preparation of
many of your favorite compact discs.
•selecting filters
The TTC provides you with 4 completely independent bell filters, a high-shelf filter, and a low-
shelf filter per channel. Let's first talk about the bell filters. You have a fairly wide range of
control on each of the parameters for the bell filters. The center frequencies range from 28 Hz
to 18 kHz, giving you 56 possible values spaced uniformly on one-sixth octave centers. The
gain at the center frequency ranges from a maximum of +12 dB boost to a minimum of -95 dB
cut. Finally, you have 12 values of slope which typically correspond to values of Q between
0.4 and 8.0. These parameters allow you to generate fairly complicated frequency-domain
profiles, ranging from precisely located notches to broad, sweeping curves. The low- and
high-shelf filters can have their corner frequencies placed at the same numerical values as the
center frequencies for the bell filters. The boost and cut similarly range from +12 dB to -95 dB.

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FIGURE 11
How to do it. With the rdq-6 in normal operating mode, the display will show all of the
parameters for the low shelf filter, filters 1, 2, 3, 4 and the hi shelf filter across the screen from
left to right. These parameters are organized in block form with the filter gain at the top,
center frequency in the middle and the slope value on the bottom line. Pressing one of the
six buttons directly underneath any of these parameter blocks will bring that filter into focus.
Figure 11 shows the rdq-6 as if the button for filter 3 had been hit (ignore for now the
particular values assumed by the various parameters). In this state, the three knobs control
the various parameters for bell filter 1; the knob below the gain display controls the amount
of boost/cut, the knob below the frequency display controls the center frequency, and the
knob below the slope display controls the slope. The audio signal is affected in real-time
when any of the parameters are changed. Pressing the button underneath EXIT will take you
back to the normal operating mode and the display for the filter you just changed will be
updated with the new parameters.
FIGURE 12
Next, press the button underneath the low shelf filter parameters. The display changes as
shown in Figure 12. Notice there is no value of slope shown; this is because the low-shelf filter
has a fixed slope, which cannot be modified by the user. The corner frequency and gain
parameters for the low-shelf filter are adjusted in the same manner as with the bell filter. The
same is true for the high-shelf filter. All six filters in each channel can be set in this manner;

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press the button corresponding to the filter of interest in order to display its parameters and
bring the focus of the knobs to that particular filter.
It is important to realize that the display will change whenever you change which channel is
in focus. This is because the display is not large enough to show the parameters for all six
filters and the volume for all six channels at once. Think of the channel select button as
serving to “bring the focus” of the knobs and display to the active channel represented.
memoryfunctions
The rdq-6 gives you the ability to store and recall up to 49 configurations. Furthermore, there
are a number of useful functions that allow you to compare presets against one another. This
section describes how to use the rdq-6's preset facility.
•save preset
FIGURE 13
How to do it. Suppose you have dialed in the rdq-6's controls to a setting you find pleasing:
you are happy with the bell filters, the shelf filters, the input, and the dither for all six
channels. You can save this setting so it can be recalled at a later time or so that you can
experiment further without worrying about not being able to return to this state. To save this
setting, press the system button and select the SAVE submenu. The rdq-6's display will
appear as in Figure 13. Use the knob beneath the numeric display to choose a preset number.
Once you select a number, press the button directly underneath SAVE. After a short amount
of time, you should see a confirmation of the save operation. To return to the system menu,
press the BACK button or press EXIT to return to normal operation.

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•load preset
FIGURE 14
How to do it. Now that we know how to store presets, what about recalling them?
Assuming we are in the normal mode of operation, press the system button and select the
LOAD submenu. The display will appear as in Figure 14. Notice that there are two numbers
shown: aand b. These two numbers allow you to compare two presets against one another.
For example, suppose you previously created two presets that you liked and saved them as
presets 7 and 4, respectively. To compare them with one another, use the knobs beneath the
displays to set ato 7 and bto 4. To listen to preset 7 (the apreset), press the LOAD A button.
This will load preset 7 and put indicators next to the adisplay. To listen to preset 4, press the
LOAD B button. This will load preset 4 and put indicators next to the bdisplay. You can
toggle between presets 7 and 4 by pressing the LOAD A and LOAD B buttons.
It is important to note that aand bare nothing more than "placekeepers." They can be set to
any values, even the same values. The only reason we have provided the bpreset is for
simple comparison between two settings. For example, suppose you wish to compare preset
1 with preset 49; this would be difficult without the a/b controls.
You should make note of two particular preset numbers. Loading preset number 0 will return the
rdq-6toa"flat"setting. Theflatsettingischaracterizedby:
•allbellandshelffiltersdisengagedforallsixchannels
•24-bitoutput
•stereo-linkedmodeforthefrontandsurroundprocessorcards
•volumeoffsetof0dBforallchannels
Note that preset 0 will not change the active input from the one presently engaged. All other
presetswillchangetheactiveinputtotheinputindicatedbythechosenpreset.
Preset49isimportantbecause it is theuser-defaultpreset. Inotherwords, preset 49 willbeloaded
automatically when the power is turned on. Therefore, you should store in preset 49 the settings
youwanttobeineffect(activeinput,dither,volumeoffsets,andfilters)whentheunitwakesup.

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appendixA:equalizationanddither
•equalization
The TTC consists of two types of filters: bells and shelves. These filters derive their names from
their frequency-domain shapes. The bell filter is characterized by three parameters: the
center frequency, the amount of cut (or boost), and the bandwidth. Bell filters are typically
used for applications such as resonance control, room mode control, and narrow-band noise
reduction, to name a few. The bell filter has a typical gain of 0 dB (unity gain) with a
maximum cut of -g dB occurring at the center frequency. The bandwidth, expressed in Hertz,
is defined as the width of the filter at its -3 dB points. It is typical to express the bandwidth of a
bell filter in terms of its quality factor, Q. The Q parameter is defined as the ratio of the filter's
center frequency, fc, to filter's bandwidth, BW. Formally, we have the relation
Qf
BW
c
=
We can see from this equation that for a given center frequency, as we make the bandwidth
smaller, the value of Q increases. The same discussion holds valid for bell filters in boost mode
rather than in cut mode. Rather than describing the bell filters’ bandwidths in terms of Q, we
have chosen to display on the front panel a parameter we call “slope.” Slope is related to Q in
a straightforward fashion, as detailed in Appendix B.
FIGURE 15
For most users, it will suffice to understand how the slope parameter works in a qualitative
sense. Consider the widest filter shown in Figure 15, which has a center frequency of 1000 Hz
and a cut of –6 dB. As we vary the slope while keeping the center frequency and gain
constant, the bandwidth of the filter changes. As the slope increases, the bandwidth
decreases (that is, the filter gets narrower). On the rdq-6, the slope varies from 1 to 12, with a

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slope of 1 giving the widest bandwidth, and a value of 12 giving the narrowest bandwidth.
Figure 15 illustrates this relationship clearly -- as we increase the slope parameter, the 3-dB
points will gradually move toward 1000 Hz from the left and from the right and the filter gets
narrower and narrower.
Whereas Figure 15 showed the effect of changing the slope while holding the center
frequency and gain constant, Figure 16 shows the effect of holding the slope and gain
constant while moving the center frequency. Figure 16 shows a family of frequency response
curves for a slope equal to 05, a gain of –6 dB and center frequencies of 100 Hz, 1 kHz, and 10
kHz, respectively. Notice that the filters have identical shapes when viewed on a logarithmic
frequency axis.
FIGURE 16
Finally, Figure 17 shows the effect of holding the slope and the center frequency constant
while varying the gain. In particular, the center frequency is 1000 Hz, the slope is the
minimum allowed, 01, and the gain is varied between –6 dB and +6 dB.
FIGURE 17

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So far, we’ve only discussed bell-shaped parametric filters. We will now turn our attention to
shelving filters. Whereas bell-shaped filters are used to emphasize or de-emphasize a range of
frequencies in a bell-shaped region about a center frequency, a shelving filter is used to
emphasize or de-emphasize all of the frequencies above or below a desired corner frequency.
A shelving filter is characterized by a pair of parameters: the corner frequency and the gain.
For example, consider the shelving filters shown in Figure 18. These curves correspond to a
low-shelving filter with a corner frequency of 500 Hz and gains of -2 dB, -6 dB, and -12 dB,
respectively. Ideally, a low-shelving filter would be flat until the corner frequency and drop to
a value specified by the gain for all frequencies below the corner frequency. In practice, these
filters have a finite slope, as shown in Figure 18.
The corner frequency is tough to “eyeball” from these plots. Loosely speaking, it is the
frequency at which the magnitude response deviates by 3 dB from the 0-dB reference (which
only makes sense for filters that have shelves lower than -3 dB). For example, the bottom
curve in Figure 18 is down by 3 dB at roughly 500 Hz. Below 500 Hz, the curve continues to
slope downward, approaching flatness at a level of -12 dB. We have not shown a low shelving
filter with boost instead of cut, but this too is permissible.
FIGURE 18
A high-shelving filter is similar to a low-shelving filter. The only difference is that frequencies
above the corner frequency are boost or cut. Figure 19 shows a family of curves for a high
shelving filter with a corner frequency of 5 kHz.

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FIGURE 19
•dither
In order to understand dither, we must briefly discuss the problems associated with
quantization and re-quantization. First, quantization is the process whereby a continuous-
valued analog signal is converted into a discretely valued digital signal. In the case of
compact disc digital audio, an audio signal is represented by 16-bit samples taken 44,100
times per second. A 16-bit system comprises 216=65,536 quantization steps. Thus, 16-bit
quantization consists of sampling the analog waveform uniformly in time and approximating
each sample by the nearest of the 65,536 quantization steps. Conventional quantization
begins to show its weakness on source material with wide dynamic range (i.e., a very high
ratio between the levels of the loudest sounds and the softest sounds, typical of orchestral
music). In order to make room for the loudest sounds, the quietest sounds are "pushed"
below the smallest quantization step, leading to signal-dependent quantization noise. This
distortion can manifest itself in many different ways including harshness, edginess, loss of
reverberant detail, and alteration of timbre. Loosely speaking, then, a digital audio system's
performance is bounded by a level that is established by the size of the quantization step
used.
This same type of distortion can occur when doing digital-to-digital operations, as well. For
example, to ensure a high-quality end product, many compact discs are mastered at 20 bits or
24 bits as an intermediate format for editing, equalization, compression, and level adjustment.
One of the final steps of the mastering process is to convert the 20- or 24-bit digital signal to a
16-bit signal for final release on the CD format. The problems here are more or less the same
as those associated with quantization of an analog signal. The 20- or 24-bit signal has much
wider dynamic range than the 16-bit signal and signal-dependent distortion can occur when
making the transfer to 16 bits. In this case, the mastering engineer must deal with the
problems associated with re-quantization noise.
Any type of DSP algorithm such as volume control or tone control involves mathematical
operations on an input signal which result in the accumulation of extra bits. For example, the

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internal result of the rdq-6’s volume control is, in general, 40 bits, whereas the CD source
material feeding it is only 16 bits. Ideally, we would like to present the digital-to-analog
converter (DAC) with a signal having the proper bit-width. For today’s 20-bit converters, we
need to somehow “map” the 40 internal bits to a 20-bit result that can be used by the
converter. How we do this can impact the sound dramatically. In fact, one of the keys to
successful audio DSP is dealing with the accumulated extra bits.
This is where dither comes in. Dither is an extremely low-level signal that is used to
ameliorate some of the sonically disturbing effects of quantization or re-quantization. There
are many different “flavors” of dither, all of which have their own strengths and weaknesses.
In its simplest form, dither is a very small noise signal that is added to the original signal
before quantization or re-quantization. The net result of dither is to decorrelate the
quantization or re-quantization error from the signal itself, which helps improve the low-level
characteristics of the system. It may seem paradoxical that the key to eliminating digital
distortion is through the addition of noise, but this is indeed the case. Dither will increase the
system’s overall noise level, but the resulting noise floor is much more like an analog noise
floor. Interestingly, in a properly dithered system signal details far smaller than the smallest
quantization step can be heard, giving an effective dynamic range well beyond the 96 dB
commonly attributed to the compact disc medium. This has profound sonic implications,
including but not limited to timbral neutrality, stereo image, and reverberant detail. Judicious
use of dither is one of the keys to the rdq-6’s unrivaled sonic performance.
Let’s look at a simple example. Figure 20 shows the spectrum of a 40-bit 5512 Hz sine wave
sampled at 44.1 kHz, with an amplitude of –96 dB from full-scale digital. Notice that all of the
signal’s power is concentrated at the frequency of the fundamental: 5512 Hz. There is actually
a small amount of power across the rest of the audio band due to the quantization to 40 bits,
but it is well below –160 dB in magnitude.
FIGURE 20
What happens when we convert the 40-bit sine wave to a 16-bit sine wave by means of
truncation (that is, by throwing away the lower-order bits)? Figure 21 shows the spectrum of

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the truncated sine wave. Observe that there are harmonically related features all up and
down the spectrum. When we listen to this signal, it will sound harsh and “buzzy,” like a
square wave. This makes sense intuitively: -96 dB undithered from full scale leaves us with
essentially two quantization steps, which looks like a very low-level square wave. Now,
suppose that before truncating to 16 bits we add a random noise signal (the dither) to the 40-
bit sine wave where the noise has a peak magnitude of approximately –84 dB from full scale.
This has the effect of “stimulating” more quantization levels. The result is the spectrum shown
in Figure 22. Observe that the harmonic distortion evident in Figure 21 is no longer present.
FIGURE 21
It is important to understand that we haven’t gotten something for nothing. We’ve traded
harmonic distortion for an elevated noise floor. In Figure 21, the non-harmonic components
are, for the most part, below –140 dB in magnitude. In Figure 22, we can see that the noise
level has risen to roughly –125 dB. This will be perceived as a very slight hissing sound, much
like analog tape noise. This hissing, however, is much more benign than the harmonic
distortion induced by truncation. Upon listening, the signal in Figure 21 is not recognizable
as a sine wave. The signal in Figure 22, however, sounds like a sine wave in a low-level hissing
background. The same can be said for other low-level signals, not just laboratory-produced
sine wave test signals.
This example only showed the effect of “flat” dither, which is dither with a flat power
spectrum. There are other types of dither that have different shaped power spectra. For
example, it is possible to “frequency-shape” the dither so that most of its power is contained
in the high frequencies where the ear is less sensitive to it. There are also other dithers that
have more complicated spectral shapes. Whatever the flavor of dither used, its purpose is the
same: to reduce the distortions incurred whenever a signal needs to have its number of bits
reduced.
This brings us back to the discussion of digital volume control. How is it possible, then, for the
rdq-6 to control the volume in the digital domain without any significant loss of resolution?
The answer has to do with dither. Suppose you are playing a 16-bit CD through the rdq-6 and
into a 20-bit DAC. With the volume set to 0.0 dB, the 16 bits of the CD are aligned with the 16