A still open problem in the field of room response equalization is the development of perceptually useful mixed-phase equalizers. In a recent paper, a multipoint mixed-phase room response equalization system, integrating a minimum-phase multiple position room magnitude equalizer and a FIR group delay equalizer, was developed in the frequency domain. Starting from this approach, a mixed time-frequency algorithm is here proposed. The minimum-phase multiple position equalizer developed in the frequency domain, is combined with an all-pass FIR phase equalizer, designed in the time domain considering a suitable time-reversed version of a prototype function and taking advantage of the mixing time evaluation. Several tests have been performed considering real environments and comparing the proposed approach with the previous one, based on a group delay compensation. Subjective listening tests have also been done in a real environment, confirming the improvement in the perceived audio quality.

1. Paper ID 38
Mixed Time-Frequency Approach for
Multipoint Room Response Equalization
A. Primavera1
, S. Cecchi1
, F. Piazza1
, and A. Carini2
1
A3Lab - DII - Universit`a Politecnica delle Marche
Via Brecce Bianche 1, 60131 Ancona Italy
www.a3lab.dibet.univpm.it
2
2DiSBeF - Universit`a di Urbino “Carlo Bo”
Piazza della Repubblica 13, 61029, Urbino Italy
Abstract
A still open problem in the field of room response equalization is the development of perceptually
useful mixed-phase equalizers. In a recent paper, a multipoint mixed-phase room response equal-
ization system, integrating a minimum-phase multiple position room magnitude equalizer and a FIR
group delay equalizer, was developed in the frequency domain. Starting from this approach, a mixed
time-frequency algorithm is here proposed. The minimum-phase multiple position equalizer devel-
oped in the frequency domain, is combined with an all-pass FIR phase equalizer, designed in the
time domain considering a suitable time-reversed version of a prototype function and taking advan-
tage of the mixing time evaluation. Several tests have been performed considering real environments
and comparing the proposed approach with the previous one, based on a group delay compensation.
Subjective listening tests have also been done in a real environment, confirming the improvement in
the perceived audio quality.

2. Introduction
Room response equalizers improve the objective and subjective quality of sound reproduction
systems by compensating the room transfer function.
Room Response Equalization
Two types of equalizers, minimum-phase and mixed-phase, have been proposed in the literature:
The equalizer acts on the minimum-phase part of the room transfer function phase response:
• it can compensate only the magnitude response;
• the subjective performance could be limited.
Minimum-Phase Room Equalizers
The equalizer copes also with the non minimum-phase part:
• it can remove also some of the room reverberation;
• “pre-echoes” problems may occur due to the errors in the non-causal part of the equalizer.
Mixed-Phase Room Equalizers

3. Introduction
Room equalizers are also categorized as single and multiple position:
• The equalization filter is designed on the basis of a measurement of the impulse response in a
single location;
• it achieves room equalization only in a reduced zone around the measurement.
• The impulse response varies significantly with the position and time.
• Use of complex spectral smoothing and short equalization filter is often adopted [1].
Single Position Room Equalizers
• The equalization filter is designed on the basis of a measurement of the impulse response in
different locations;
• it is capable to enlarge the equalized zone.
Multiple Position Room Equalizers

4. Proposed Structure (Magnitude)
The proposed structure is mainly composed of two parts: magnitude and phase equalizer.
Fig.1 Proposed approach both in time and frequency domain: yellow indicates the frequency domain while blue represents the time domain.
1. M IRs of N samples length are measured at different positions in the zone to be equalized.
2. The frequency responses are computed with M FFTs of length K.
3. Complex fractional octave smoothing is performed on the M frequency responses [1].
4. A prototype room magnitude response is derived taking into account all the smoothed IRs [2]:
Hp (k) =
1
M
M
i=1
Hcs,i (k) k = 0, · · · , K − 1. (1)
5. An inverse model hinv[n] for the prototype room magnitude response is obtained [3].
Magnitude Equalizer

5. Proposed Structure (Phase)
Use the time reversed version of
the obtained prototype to perform the
phase compensation operation [4, 5].
Idea
Truncate the prototype function taking
into consideration the mixing time eval-
uation.
Improvement
6. A time domain prototype is calculated taking into consideration the original IRs, suitably aligned,
and the inverse model hinv[n]:
hp[n] =
1
M
M
i=1
(hi[n] ∗ hinv[n]) . (2)
7. Mixing time evaluation considering the Kurtosis (k) and the Mean Absolute Deviation/Standard
Deviation ratio (r) [6, 7]:
k =
E(x−µ)4
σ4 − 3 r =
E(|x−µ|)
σ
t1 = t|∂k(t)
∂t →0
t2 = t|∂r(t)
∂t →0
tmix = max(t1, t2). (3)
8. The prototype function is truncated taking into consideration the mixing time evaluation.
9. The time reversed version of the impulse response is computed [4, 5].
10. Taking into consideration the previous steps, an allpass FIR filter, is designed.
Phase Equalizer

6. Experimental Results - Setup
Tests executed employing impulse responses recorded in a real environment.
Measurements have been performed using:
• MOTU sound card;
• AKG microphones with an omnidirectional
response;
• Genelec loudspeaker;
• PC running the NU-Tech platform to man-
age all I/Os [8].
Professional Equipment
The impulse responses have been derived
using:
• logarithmic sweep signal excitation;
• 48 kHz sampling frequency.
Impulse Responses Identification
Fig.2 Loudspeakers and microphones positions in the room.
• Magnitude equalization [9, 10].
• Magnitude and group delay equalization
[9, 10].
• Magnitude and phase equalization (pro-
posed approach).
Compared Equalizers

7. Experimental Results - Objective Evaluation (Magnitude)
• Frequency range of equalization: 50-16000Hz;
• Target curve: flat.
Fig.3 Magnitude response of the measured IRs and frequency response of the magnitude equalization filter (EQ).
Good results are obtained in terms of inversion, taking into consideration that the equalizer is
derived by a set of IRs.
Considerations

8. Experimental Results - Objective Evaluation (Phase)
Fig.4 Phase distortion after (a) the magnitude equalization, (b) group
delay compensation method and (c) the phase equalization approach.
Evaluation of the group delay variation:
GDD =
1
M
M
l=1
1
Qh − Ql + 1
Qh
i=Ql
GDl(i) − Kl
2
, (4)
with:
Kl =
1
Qh − Ql + 1
Qh
i=Ql
GDl(i) , (5)
where:
• Ql, Qh are the lowest and the highest fre-
quency of the equalized band;
• GDl is the group delay of the M IRs.
Not Magnitude Group Delay Phase
Equalized Equalizer Equalizer Equalizer
76.70 80.16 45.79 42.11
Tab.1 Mean group delay deviation measures

9. Experimental Results - Subjective Evaluation
To assess the overall audio quality perception of the equalization procedure, subjective listening tests
were performed [11] (considering 8 expert listeners, 4 experiment, 3 algorithms).
Fig.5 Graphical User Interface used for the listening tests.
Music Author Sound Track
Genre
Rock ZZtop Concrete and steel
Popular Donald Fagen I.G.Y
Jazz Nina Simone My baby just cares for me
Classical Ciaikovski Nutcracker Suite op.71a
Tab.2 List of sound tracks used for the listening tests.
Fig.6 Results of listening test considering the mean value and the
confidence intervals.
The results show an overall improvement of the
proposed approaches compared with the un-
equalized signal.
Considerations

10. Conclusions
• A multiple position mixed-phase equalizer has been proposed in the paper.
• The equalizer has been obtained by combining a room magnitude equalizer with a phase equalizer.
– The magnitude equalizer is designed in the frequency domain averaging and smoothing the room magnitude
responses.
– The phase equalizer is derived in the time domain, taking into consideration the mixing time and the time reversed
version of the obtained prototype.
• The proposed approach has been compared with a previous method, based on the group delay compensation, to
investigate the performance of two different approaches.
• Objective and subjective comparisons have shown comparable performance between the two approaches, and
most of all good performance in terms of sound quality enhancement, taking into consideration a real environment.
References
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