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Goldmund White Paper
PROTEUS 2-CHANNEL:
THE MOST POWERFUL INVENTION IN AUDIO HISTORY
The primary objective of the Proteus project was to develop a technology that would allow us
to make the most perfect speaker on earth.
This took the company 7 years of painstaking Research & Development efforts and resulted in
the creation of the Epilogue 1 Signature. But our acoustic laboratory was prompt to discover
that Proteus could also be applied to many other speakers (even those manufactured by other
brands), optimizing their performance and producing a sound
• With an incredible spaciousness,
• Where each instrument positioned at its correct place,
• With a complete stability of the image,
• With perfectly well defined trebles,
• With extremely neat bass,
• With ultra high definition and precision in the voices’
• With much higher playback levels without distortion
What this means in short is that a system using Proteus provides the most lifelike sound that
anyone has ever heard.
Many tests have been performed by High End specialists where the performance and sound
qualities of the same system are compared with and without the Proteus Technology. They are
unanimous on the improvements brought and some have qualified Proteus as
“the most powerful invention in audio history”.
“Perfection in an imperfect world”

The basic idea of the Proteus technology is to optimize a speaker’s performance by reproducing its
original passive filter in the digital domain.
Phase distortion, varying speaker load, and component tolerance are inherent to physical filters and
affect the quality of the sound reproduction at different levels. Digital filters resolve these issues by the
impossibility to be affected by material elements and by the inexistence of physical constraints.
Digital filters are calculated thanks to the Proteus mathematical model that integrates all the technical
parameters of the original filter and delivers digital configurations that are loaded within a Goldmund
Acoustic Processor (Mimesis 16, 16HD, 32 or Metis 10), in a Goldmund amplifier DSP board, or in
Goldmund customized processors used in analog systems.
They offer four advantages:
1. They are much more precise.
2. The amplifiers are directly connected to each driver (the speaker’s passive filters are
bypassed) which provides a much better control over them and a better amortization.
3. They allow the use of speakers at a much higher volume level without distortion.
4. They also open capabilities to correct the driver much more accurately than it could be done
with a passive crossover (such corrections are only made with the agreement of the speaker
manufacturer).
Proteus positions Goldmund as the only company in the world able to create a stereo system
completely corrected in:
• Amplitude
• Phase
• Time
In audio more than any other domain, time is of the essence. A proper time alignment is crucial in
what we call the Recognition Factor, which is the ability of our brain to recognize a sound as real (high
recognition factor) vs. reproduced (low recognition factor). The time alignment technology used in
Proteus is called the Leonardo Time Correction (see the white paper explaining Leonardo further
down). In a system that does not use Proteus the listener’s brain concentrates on reconstructing the
time alignment of a sound that it perceives as un-natural (time distortion does not exist in nature). In a
Proteus system this action is performed by the audio system itself, leaving the brain focus on the
music itself and on the true emotion that a completely natural sound brings to each passionate music
listener.
Today, the Proteus technology has also been extended to complete home theater system, where
each driver is “managed” by Proteus but where what results of the sum of all drivers within a system is
also perfectly optimized to correct the acoustic of the room itself. This is the Goldmund Media Room
concept.
Related web pages:
Goldmund Acoustic Processors:
http://www.goldmund.com/products/mimesis_32
http://www.goldmund.com/products/mimesis_16hd
http://www.goldmund.com/products/mimesis_16
http://www.goldmund.com/products/metis_10
The Goldmund Media Room:
http://www.goldmund.com/media_room
“Perfection in an imperfect world”

Goldmund White Paper
LEONARDO
GROUP DELAY DISTORTION AND CORRECTION
SOLUTIONS
The Example of the Epilogue 1 crossover Correction
Within the framework of the Leonardo project, we decided to establish whether sounds
are likely to be affected by phase distortion. We will see in the next section why, in our
case, we can call this kind of distortion: ”group delay distortion”. A theoretical study
and appropriate listening experiments demonstrated justifiably that these effects have
not to be neglected. It was decided then to analyse the group delay distortions
produced by our loudspeaker systems with the aim of correcting them.
“Perfection in an imperfect world”

THE EXAMPLE OF THE EPILOGUE 1 CROSSOVER CORRECTION
A two-way vented loudspeaker system such as the Epilogue 1 shows three main group delay
distortion sources:
- the high-pass filter resulting from the medium and port alignment,
- the low-pass filter resulting from the tweeter high cut-off frequency,
- and the electrical internal crossover.
It appeared that the most noticeable group delay distortion effect was the one produced by the
electrical crossover. It was then decided to study first in detail this kind of distortion with the aim
of providing a solution to correct it.
The purpose of this paper is to explain our approach of group delay distortion correction,
according to the concrete example of the Epilogue 1 crossover specifications.
The figure below is illustrative of group delay distortion phenomenon. It shows the time
modification of a half-squared signal passing through the Epilogue 1 internal crossover.
It is worth noting that the amplitude frequency responses of these two signals are absolutely
identical. The sole difference comes from the phase response behaviour.
GROUP DELAY DISTORTION THEORY
This section constitutes a summary of accepted equations defining the phenomenon of
group delay distortion. Readers familiar with this material can go straight to the next
section.
Impulse response:
Frequency response:
1 ∞
jwt
h( t)
= ∫ H ( w)
e dw
2π
− ∞
∞
− jwt
H ( w)
=
∫ h(
t)
e dt = H ( w)
e
− ∞
“Perfection in an imperfect world”
jϕ
( w)

There are two kinds of group delay distortion:
1. Minimum phase (for any |H(w)|):
min
If |H(w)| ≠ K (cst) ⇒ linear distortion
(module)
If ϕ(w) ≠ -wt ⇒ group delay
distortion
1 ∞ ln H ( w')
( w) = ∫ dw'
π
− ∞
w'−w
ϕ (Hilbert equation)
ϕ ( ) = θ ( w)
− wT + θ
w ap
2. Phase excess: excess
0
with: θap(w) all-pass phase delay (~f)
-wT pure delay (propagation) (~f)
θ0 phase delay (not ~f)
To go further into detail, we can add to our study a third phase distortion, which is not
a group delay distortion, called the “phase-intercept distortion”. This distortion may
happen at the initial condition t=0, even if ∆τg(w) = 0. Given that the latter is nonexistent
in our case, we are authorized to use the term of “group delay distortion” as a
generic term for phase distortion.
In conclusion, we can say that the group delay distortion we have to correct is due to
the parameters: ϕmin(w), θap(w) and θ0.
As we are describing group delay distortion, it is more convenient to represent it
directly from the group delay quantity:
∆τ
( w)
− dϕ(
w)
− d(
ϕ
τ g ( w)
= =
dw
min
g
( w)
+ θ
64
44 74448
ap ( w)
− wT + θ 0 )
= T + τ min ( w)
+ τ excess ( w)
dw
123
14243
“Perfection in an imperfect world”
minimum
The approach we have chosen comprises correcting the group delay distortion as a whole.
To simplify, we can write the group delay as:
τ ( ) = T + ∆τ
( w)
g
w g
The aim of the phase correction is to add a new group delay, enabling the frequency
dependent term ∆τg(w) to be compensated without modifying the amplitude response:
τ
( w ) = T + ∆τ
( w)
+ T − ∆τ
( w)
= T + T
g
g
g
g
g
excess

To illustrate the equations, the figure below shows the impulse and frequency responses of the
all-pass filter simulating the group delay behaviour of the Epilogue 1 crossover.
“Perfection in an imperfect world”
τ ( ) = ∆τ
( w)
g
w g
As we can see, the impulse signal entering the all-pass filter (black curve) is
significantly modified (red curve) in spite of a flat amplitude level. This behaviour is
explained by the fact that the group delay is not constant according to the frequency.
The figure below shows the response of the same all-pass filter for a delayed entering
impulse signal.
τ ( ) = T + ∆τ
( w)
g
w g
As we can see, the modification of the impulse signal is the same, excepted that it has
been delayed in time. That means that a pure delay T corresponding to the number of
delayed samples, has been added to the previous filter group delay response.

CORRECTION OF THE EPILOGUE 1 CROSSOVER GROUP DELAY DISTORTION
In the case of the Epilogue 1, it is worth noting that the internal crossover has been
calculated in order to obtain a flat on-axis frequency response. That means that the
crossover compensates some irregularities peculiar to the medium and tweeter
frequency responses. It is therefore important to correct only the group delay response
of the Epilogue 1 crossover without touching its amplitude response.
To do that, the first step comprises determining an all-pass filter having a group delay
response corresponding to that of the Epilogue 1 crossover.
We have then to calculate the behaviour in amplitude and phase of the Epilogue 1
crossover. The electrical circuit below enables the crossover to be calculated according
to resistive loads of 8.2 ohm.
V3
Rgf
0
R4
0
C1
L1
C6
L4
C3
R1
R2
L2
C7
C2
“Perfection in an imperfect world”
L5
R6
R14
C5
C8 R13
A calculation sheet has been implemented under Matlab, enabling the all-pass filter to
be determined according to the Epilogue 1 crossover group delay response. The all-pass
filter is determined by its resonance frequency and its group delay at this frequency.
R3
R5
Remf
8.2
Retwf
8.2

The figure below shows this implementation. This calculation sheet shows, for two
different squared signals, the frequency and time responses of:
- the Epi1 crossover amplitude (black curves)
- the Epi1 crossover phase and group delay distortions (blue curves)
- the all-pass filter approximating the crossover phase and group delay (red
curves)
- the result after group delay correction (pale blue curves)
The latter comes from the multiplication of the Epi1 all-pass crossover by the inversed
of the determined all-pass filter (coefficient inversion).
Now, and in order to take into account the real electrical, mechanical and acoustical
loads of the Epilogue 1 system, it is important to readjust the all-pass filter according to
the equivalent electrical circuit illustrated below.
“Perfection in an imperfect world”

Rgf
V3
0
R4
C1
L1
0
C6
C3
R1
R2
L4
L2
C7
C2
R6
C5
Letwf
Htwf
+ -
Bl
mmsmf
R14 mmstwf Rmstwf
L5
R3
C8
R5
R13
Remf
Retwf
Lemf
Hf
+ -
Bl
Hfb
-Bl
+
-
Htwfb
-Bl
+
-
Rmsmf
“Perfection in an imperfect world”
0
Cmsmf
Cmstwf
Ef
+
-
Sd
Etwf
+
-
Sd
+
-
+
-
Ff
-Sd
0 0
Ftwf
-Sd
marf
Cabf
martwf
0
Rapf
mapf

As explained above, the correction of the Epilogue 1 group delay distortion comes from
the multiplication of its all-pass crossover by the inverse of the chosen all-pass filter
(coefficient inversion).
In the case of IIR filters (chosen for their coefficient number), the transfer function of
the determined all-pass filter may be written as:
M
∑
bm
z
m=
0
H ( z)
= N
a z
The correction filter will be written simply by inverting the coefficients:
H
−1
∑
n=
0
∑
∑
m=
0
−m
−n
“Perfection in an imperfect world”
N
n
an
z
n=
0
( z)
= M
b z
The figure below shows the frequency responses (amplitude, phase and group delay) of
H(z) in magenta and 1/H(z) in red.
m
−n
−m

As we can see, the result of the summation of group delays is equal to zero. The group
delay distortion has then been properly corrected.
This filter, however, cannot be implemented as it is, due to its non-causal behaviour.
This property is demonstrated by the negative group delay curve, meaning that the
correction filter 1/H(z) responds before it receives its triggering signal, which is
obviously not possible.
Moreover, the figure below shows that the all-pass correction filter is also unstable. It
is illustrated by the fact that its poles are outside the unity circle, meaning that its
impulse response goes toward infinity (red curve).
In conclusion, we can say that our IIR correction all-pass filter is non-causal and
unstable.
If it is possible to render it causal by introducing a delay before its transfer function, it
is impossible to render it stable without touching its amplitude and degrading its phase
response.
The solution to this significant problem is provided by the time reversal method.
“Perfection in an imperfect world”

TIME REVERSAL METHOD
The purpose here is not to explain this method in detail. People interested in analysing
this in greater depth can consult us.
This solution offers the advantage of calculating the IIR filter H(z) instead of its noncausal
and unstable inverse. The inversion is carried out by inversing the samples
before and after the filter H(z).
The complete method has been implemented under Simulink and Matlab in order to
verify the theory with the view of a DSP implementation. The figure below shows the
Simulink block diagram implementation.
signal.wav
signal
up
z -50
down
z -50
In1 Out1
Phase EPI1
clr_up
In
Push
Stack Out
Pop
Clr
clr_down
In
Push
Pop
Clr
Stack Out
num1
num2
X_filt.wav
sig_filt
xr_inv
xr1_inv
Rst
50
Rst 50
xr2_inv
rst_up
In1 Out1
Phase EPI1 (up)
rst_down
In1 Out1
Phase EPI1 (down)
yyr1_filtre
z -50
yyr2_filtre
Rst 50
Rst 50
“Perfection in an imperfect world”
yr1_filtre0
z -100
yr1_filtre
yr2_filtre
yr
Y_inv.wav
In1 Out1
Phase EPI1 (v)
In
Push
Pop
Clr
Stack Out
In
Push
Pop
Clr
Stack Out
Y_correct.wav
The input signal is acquired in consecutive sections of the length L samples.
The sections are time reversed (input LIFO buffers) and separated in two signals (the
sections are taken half the time and completed by zeros to form sections of the length
2L samples).
Both signals are filtered by identical causal and stable IIR all-pass filters, which are
initialised at each double section beginning.
Both filtered signals are recombined in leading and trailing sections. The leading
sections signal is delayed of 2L samples. Both resulting signals are adding together.
The sections are again time reversed (output LIFO buffers).
y_corr
y

The figure below show the curves (calculated under Matlab) related to the different
block outputs.
The yellow curve gives the response of the Epilogue 1 crossover excited by the
superposed red input signal.
After time reversal computation, the correction all-pass filter is given by the blue curve.
In order to verify the group delay correction made by this filter, all we have to do is to
cascade the all-pass correction filter (blue) and the all-pass crossover (yellow).
The result is given by the last red curve. As we can see, this curve shows a very high
degree of accuracy compared to the excitation signal. The small 4L delay comes from
the implementation buffers. These calculations validate the time reversal method.
“Perfection in an imperfect world”

The method has been then programmed in DSP following the block diagram below.
input
in_inv buffer out_inv output ( delay = 4L)
0
0
0
F1
F2 reset
0
F1 reset
F2 reset
0
F1 reset
F2 reset
0
F2
F2
F2
F1
F1
F1
“Perfection in an imperfect world”

The figure below shows the DSP computed response of the correction all-pass filter (in
blue) for a step excitation (in red).
As we can see, the blue curve fits well with the one calculated previously during the
method validation step.
This result concludes with success the first stage of the Leonardo project. We have
carried out some preliminary demo listening tests and we can say that the results are
extremely impressive...
REFERENCES
S.A. Azizi. Realization of linear phase sound processing filters using zero phase IIR
filters. AES preprint 4506, March 1997.
D. Koya. Aural phase distortion detection. Thesis submitted to the University of Miami,
May 2000.
S.R. Powell and P. M. Chau. A technique for Realizing Linear Phase IIR Filters. IEEE
Transactions on signal processing, 39(11): 2425-2435, November 1991.
“Perfection in an imperfect world”