Paper ID 38

Mixed Time-Frequency Approach for

Multipoint Room Response EqualizationA. Primavera1, S. Cecchi1, F. Piazza1, and A. Carini2

1A3Lab - DII - Universita Politecnica delle MarcheVia Brecce Bianche 1, 60131 Ancona Italy

www.a3lab.dibet.univpm.it22DiSBeF - Universita 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 perceptuallyuseful 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 FIRgroup delay equalizer, was developed in the frequency domain. Starting from this approach, a mixedtime-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 thetime 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 environmentsand 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 inthe perceived audio quality.

Introduction

Room response equalizers improve the objective and subjective quality of sound reproductionsystems 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

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 asingle 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 indifferent locations;• it is capable to enlarge the equalized zone.

Multiple Position Room Equalizers

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

Proposed Structure (Phase)

Use the time reversed version ofthe obtained prototype to perform thephase compensation operation [4, 5].

Idea

Truncate the prototype function takinginto 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/StandardDeviation 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

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 derivedusing:• 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

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 isderived by a set of IRs.

Considerations

Experimental Results - Objective Evaluation (Phase)

Fig.4 Phase distortion after (a) the magnitude equalization, (b) groupdelay 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 PhaseEqualized Equalizer Equalizer Equalizer

76.70 80.16 45.79 42.11

Tab.1 Mean group delay deviation measures

Experimental Results - Subjective Evaluation

To assess the overall audio quality perception of the equalization procedure, subjective listening testswere performed [11] (considering 8 expert listeners, 4 experiment, 3 algorithms).

Fig.5 Graphical User Interface used for the listening tests.

Music Author Sound TrackGenreRock ZZtop Concrete and steel

Popular Donald Fagen I.G.YJazz 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 theconfidence intervals.

The results show an overall improvement of theproposed approaches compared with the un-equalized signal.

Considerations

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 magnituderesponses.

– The phase equalizer is derived in the time domain, taking into consideration the mixing time and the time reversedversion of the obtained prototype.

• The proposed approach has been compared with a previous method, based on the group delay compensation, toinvestigate the performance of two different approaches.

• Objective and subjective comparisons have shown comparable performance between the two approaches, andmost of all good performance in terms of sound quality enhancement, taking into consideration a real environment.

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[10] S. Cecchi, L. Romoli, F. Piazza, and A. Carini, “Multipoint Room Response Equalization with Group Delay Compensation: Subjective Listening Tests,” in Proc. IEEE 7th International Symposium on Imageand Signal Processing and Analysis (ISPA’11), Dubrovnik, Croatia, Sep. 2011.

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