PAPERS 0 INTRODUCTION A loudspeaker installed in a room acts as a coupled sys- tem where the room properties typically dominate the rate of energy decay. At high frequencies, typically above a few hundred hertz, passive methods of controlling the rate and properties of this energy decay are straightforward and well established. Individual strong reflections are bro- ken up by diffusing elements in the room or trapped in absorbers. The resulting energy decay is controlled to a desired level by introducing the necessary amount of absorbance in the acoustical space. This is generally feasi- ble as long as the wavelength of sound is small compared to the dimensions of the space. As we move toward low frequencies, passive means of controlling the speed of reverberant decay become more difficult to use because the physical size of the necessary absorbers increases and may become prohibitively large compared to the volume of the listening space, or absorbers have to be made narrow-band. Consequently the cost of passive control of reverberant decay greatly increases at low frequencies. Methods for optimizing the response at a listening position by finding suitable loca- tions for loudspeakers have been proposed [1] but cannot fully solve the problem of controlling modal decay. Because of these reasons, and because active control becomes technically feasible when the wavelength of sound becomes long relative to the room size, resulting in a less diffuse sound field in the room [2]–[6], there has been an increasing interest in methods of active sound- field control at low frequencies. Mode resonances in a room can be audible because they modify the magnitude response of the primary sound or, when the primary sound ends, because they are no longer masked by the primary sound [7], [8]. The detection of a mode resonance appears to be very dependent on the sig- nal content. Olive et al. report detection thresholds for res- onances for both continuous broad-band sound and tran- sient discontinuous sound, showing that low-Q resonances are more readily audible with continuous signals contain- ing a broad frequency spectrum whereas high-Q reso- nances become more audible with transient discontinuous 324 J. Audio Eng. Soc., Vol. 51, No. 5, 2003 May Modal Equalization of Loudspeaker – Room Responses at Low Frequencies * AKI MÄKIVIRTA, 1 AES Member, POJU ANTSALO, 2 MATTI KARJALAINEN, 2 AES Fellow, AND VESA VÄLIMÄKI, 2 AES Member 1 Genelec Oy, FIN-74100 lisalmi, Finland 2 Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing, FIN 02015 HUT, Espoo, Finland The control of excessively long decays in a listening room with strong low-frequency modes is problematic, expensive, and sometimes impossible with conventional passive means. A systematic methodology is presented to design active modal equalization able to selectively reduce the mode decay rate of a loudspeaker–room system at low frequencies in the vicinity of a sound engineer’s listening location. Modal equalization is able to increase the rate of initial sound decay at mode frequencies, and can be used with conventional magnitude equal- ization to optimize the reproduced sound quality. Two methods of implementing active modal equalization are proposed. The first modifies the primary sound such that the mode decay rates are controlled. The second uses separate secondary radiators and controls the mode decays with additional sound fed into the secondary radiators. Case studies are presented of imple- menting active modal control according to the first method. * Manuscript received 2002 July 15; revised 2003 February 14. Parts of this paper were presented at the 111th Convention of the Audio Engineering Society, New York, 2001 November 30–December 3.