Mixed Time Frequency Approach for Multipoint Room Response Equalization

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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.

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Mixed Time Frequency Approach for Multipoint Room Response Equalization

  1. 1. Paper ID 38Mixed Time-Frequency Approach forMultipoint Room Response EqualizationA. Primavera1, S. Cecchi1, F. Piazza1, and A. Carini21A3Lab - DII - Universit`a Politecnica delle MarcheVia Brecce Bianche 1, 60131 Ancona Italywww.a3lab.dibet.univpm.it22DiSBeF - Universit`a di Urbino “Carlo Bo”Piazza della Repubblica 13, 61029, Urbino ItalyAbstractA 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.
  2. 2. IntroductionRoom response equalizers improve the objective and subjective quality of sound reproductionsystems by compensating the room transfer function.Room Response EqualizationTwo 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 EqualizersThe 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. 3. IntroductionRoom 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
  4. 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) =1MMi=1Hcs,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. 5. Proposed Structure (Phase)Use the time reversed version ofthe obtained prototype to perform thephase compensation operation [4, 5].IdeaTruncate the prototype function takinginto consideration the mixing time eval-uation.Improvement6. A time domain prototype is calculated taking into consideration the original IRs, suitably aligned,and the inverse model hinv[n]:hp[n] =1MMi=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)4σ4 − 3 r =E(|x−µ|)σt1 = t|∂k(t)∂t →0t2 = t|∂r(t)∂t →0tmix = 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. 6. Experimental Results - SetupTests executed employing impulse responses recorded in a real environment.Measurements have been performed using:• MOTU sound card;• AKG microphones with an omnidirectionalresponse;• Genelec loudspeaker;• PC running the NU-Tech platform to man-age all I/Os [8].Professional EquipmentThe impulse responses have been derivedusing:• logarithmic sweep signal excitation;• 48 kHz sampling frequency.Impulse Responses IdentificationFig.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. 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 isderived by a set of IRs.Considerations
  8. 8. 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 =1MMl=11Qh − Ql + 1Qhi=QlGDl(i) − Kl2, (4)with:Kl =1Qh − Ql + 1Qhi=QlGDl(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 Equalizer76.70 80.16 45.79 42.11Tab.1 Mean group delay deviation measures
  9. 9. Experimental Results - Subjective EvaluationTo 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 steelPopular Donald Fagen I.G.YJazz Nina Simone My baby just cares for meClassical Ciaikovski Nutcracker Suite op.71aTab.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
  10. 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 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.References[1] P. D. Hatziantoniou and J. N. Mourjopoulos, “Generalized Fractional Octave Smoothing of Audio and Acoustic Responses,” J. Audio Eng. Soc., vol. 48, no. 4, pp. 259–280, Apr. 2000.[2] A. Carini, I. Omiciuolo, and G. L. Sicuranza, “Multiple position room response equalization: Frequency domain prototype design strategies,” in Proc. 6th International Symposium on Image and SignalProcessing and Analysis (ISPA’09), Saltzburg, Austria, Sept. 2009, pp. 633–638.[3] S. Bharitkar and C. Kyriakakis, Immersive Audio Signal Processing, Springer, New York, 2006.[4] B. D. Radlovi´c and R. A. Kennedy, “Nonminimum-phase equalization and its subjective importance in room acoustics,” IEEE Trans. Speech and Audio Processing, vol. 8, no. 6, pp. 728–737, Nov. 2000.[5] D. Preis, “Phase distortion and phase equalization in audio signal processing-a tutorial review,” J. Audio Eng. Soc, vol. 30, no. 11, pp. 774–794, 1982.[6] A. Primavera, S. Cecchi, L. Palestini, F. Piazza, and M. Moschetti, “A Hybrid Approach for Real-Time Room Acoustic Response Simulation,” in Proc. 128th Audio Engineering Society Convention (AES’10),London, UK, May 2010.[7] A. Primavera, S. Cecchi, P. Peretti, L. Romoli, and F. Piazza, “An Advanced Implementation of a Digital Artificial Reverberator,” in Proc. 130th Audio Engineering Society Convention (AES’10), London,UK,May. 2011.[8] A. Lattanzi, F. Bettarelli, and S. Cecchi, “NU-Tech: The Entry Tool of the hArtes Toolchain for Algorithms Design,” Prof. of 124th AES Convention, May 2008.[9] A. Carini, S. Cecchi, and L. Romoli, “Multipoint Room Response Equalization with Group Delay Compensation,” in Proc. International Workshop on Acoustic Echo and Noise Control (IWAENC’10), TelAviv, Israel, Sep. 2010.[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.[11] ITU-R BS. 1284-1, “General methods for the subjective assessment of sound quality,” Geneva, 2003.

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