ARMA modeling of a room transfer function at low frequencies.

Abstract

equal to the number of poles. 3. Measured impulse responses Impulse responses were measured in an experimental room, changing the reverberation time. The room was rectangular with a volume of 87 m3. The rever-beration time was set to 0.3, 0.36, 0.55, 1.6, and 2.4 s in the 500 Hz octave band by adding or removing ab-sorbing materials to or from the walls. The upper frequency of the signal bands was changed to 100, 200, 300, 400, 500, 600, 800, and 1,000 Hz. The lower frequency of the bands was fixed to 60 Hz. The sampling frequency was 2.5 times the upper frequency of the frequency band. An example of the impulse responses is shown in Fig. 1. 4. ARMA modeling of the measured impulse re-sponses The measured impulse responses were modeled by a series-parallel type ARMA model as shown in Fig. 2. The ARMA model coefficients were estimated using the RLS algorithm5) so as to minimize the error e(k) between the real echo and the estimated echo. The order of the ARMA model (P+Q) was determined such that the power of the error e(k) normalized by the power of the real echo y(k) was -40 dB. Figure 3 shows experimental results. The vertical axis represents the orders of the ARMA and the MA models that give a ratio of the error power to the real echo power of -40 dB. The horizontal axis represents the tap length of the measured impulse responses where the reverberation level drops by -40 dB. Since the order of the MA model directly corresponds to the tap length of the impulse responses, the MA model requires as many taps as the impulse response has. On the other hand, the order of the ARMA model is found to be smaller than that of the MA model, especially for the low frequency band. For example, when modeling an impulse response whose band is from 60 200 Hz for a reverberation time of 1.8 s, the MA model re-quires 600 taps, but the ARMA model requires only 240 taps. In each frequency band, when the rever-beration time is long, the ARMA model can effectively reduce the orders. These results show that the ARMA model is more effective in the low frequency band and for long reverberation times for reducing the number