Quantification of spectral shift and broadening induced by out-of-band modes in the transient process of room sound field

Abstract

The spectral structures of sound fields in rooms differ between steady-state conditions and transient processes. This study presents a methodology to enable analysis of the spectral characteristics of the transient processes of room sound fields. The energy spectra appearing during the decay and growth processes for sinusoidal and white noise excitations are formulated by redefining energy-time functions in reference to previous findings. The derived formulae present a unified approach for the interrupted sine and noise methods. The energy spectrum is used to examine the spectral shift and broadening induced by out-of-band modes during transient processes. Frequency statistics, spectral bandwidth, and band energy ratios are introduced as physical indices. The proposed method was applied to analyze the decay process of actual room sound fields following preliminary examinations using room impulse responses generated by numerical simulations. The results indicate that the effect of out-of-band modes was insignificant when the product of the excitation bandwidth and reverberation time exceeded 18 and 36, respectively, in cases with and without acoustic modal overlap. Band limiting of the received signal may not always be necessary under these conditions. In concert halls, this condition was satisfied even when the excitation bandwidth was a 1/12 octave. Thus, the physical indices introduced in this study can characterize sound fields in different rooms from an unconventional perspective.