A multichannel and multiple position adaptive room response equalizer in warped domain: Real-time implementation and performance evaluation S. Cecchi a,⇑ , L. Romoli a,1 , A. Carini b,1 , F. Piazza a,1 a Department of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy b DiSBeF, Università di Urbino ‘‘Carlo Bo’’, Piazza della Repubblica 13, 61029 Urbino, Italy article info Article history: Received 22 October 2013 Received in revised form 14 February 2014 Accepted 24 February 2014 Available online 27 March 2014 Keywords: Adaptive equalization Room equalizer Channel decorrelation Impulse response identification abstract Room response equalization systems are used for improving the listening experience in cinema theatres, home theatres, car hi-fi systems. In this paper, an adaptive multichannel and multiple position room response equalization system and its real-time implementation are described. An adaptive and accurate estimation of the room responses is provided introducing a normalized least mean square optimization approach with a variable step-size, and taking advantage of an interchannel coherence reduction tech- nique based on the missing fundamental phenomenon. Then, the equalizer is designed in warp frequency domain for improving equalization in the low frequency region, reducing the computational cost of the design procedure, and deriving an algorithm capable of working in real time. Indeed, a real-time imple- mentation of the proposed adaptive equalizer has been obtained on NU-Tech framework and has been used in order to provide a deep objective and subjective evaluation of the equalization system. The results of these evaluations illustrate the effectiveness of the proposed approach, also in comparison with other techniques of the state of the art. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Room response (RR) equalization systems are used in cinema theatres, home theatres, car hi-fi systems in order to improve the listening experience by compensating the room transfer function from the loudspeaker system to the listener [1]. In the context of audio processing, this is a very challenging task since many issues have to be faced [2]. Indeed, the design of RR equalizer must take into account that the room response varies with position [3] and with time [4], and that the room transfer function is non-minimum phase. Different RR equalization solutions has been proposed in the literature in order to cope with these factors. RR equalizers are classified as single position [5] or multiple po- sition equalizers [1]. In single position RR equalizers, the equaliza- tion filter is designed on the basis of a measurement of the room response in a single location [5], thus achieving room equalization only in a reduced zone of the size of a fraction of the acoustic wave- length around the measurement point. Therefore, a multiple posi- tion RR equalizer is considered in order to enlarge the equalized zone: differently from the single position case, the equalization fil- ter is estimated on the basis of different measurements of the room response in the zone to be equalized. More in details, many of the RR equalization systems proposed in the literature discuss fixed equalizers, designed a priori before filtering operation [1,6–11]. On the other hand, the room is a time-varying environment (a ‘‘weakly non-stationary’’ system as defined in [4]) that changes with temperature, pressure, move- ment of people, and other obstacles in the enclosure. Thus, adap- tive solutions suitable to track and correct slow variations in the room response should be adopted. Different adaptive RR equaliza- tion techniques have been proposed in the literature [12–18].A first adaptive equalizer was proposed in [12], where the equalizer is designed by adaptively minimizing the sum of the squared errors between the equalized responses and a delayed version of the in- put signal. Unfortunately, the approach of [12] is very sensitive to peaks and notches in the room response and to the room re- sponse variations at different positions. As a consequence pre-echo problems can easily be experienced with that approach. To im- prove the convergence speed and the robustness of the adaptive identification algorithm in presence of low signal to noise ratio, the use of a biased adaptive algorithm has been recently proposed http://dx.doi.org/10.1016/j.apacoust.2014.02.011 0003-682X/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel./fax: +39 0712204453. E-mail addresses: s.cecchi@univpm.it (S. Cecchi), l.romoli@univpm.it (L. Romoli), alberto.carini@uniurb.it (A. Carini), f.piazza@univpm.it (F. Piazza). 1 Tel./fax: +39 0712204453. Applied Acoustics 82 (2014) 28–37 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust