ICSV 14 Cairns • Australia 9-12 July , 2007 PROPAGATION PHASE REPRESENTATION IN 3 D SPACE USING POLES AND ZEROS IN COMPLEX FREQUENCY PLANE
This paper describes the transfer function, including the coherent sound field, as the increased distance between source and observation points, from the point of view of the number of zeros in the complex frequency plane. The authors estimated the propagation phase obtained by linear regression analysis of the narrow-frequency-band phase characteristics of the minimumphase component of the transfer function. The direct sound field estimated from the propagation phase of the minimum-phase characteristics consequently seems to be the coherent field within the critical distance. We determined that the zeros drift based on complex-integration analysis. When the sound source distance (SSD) increases, the zeros move toward a higher frequency; thus, an accumulated phase is produced following the propagation phase. When the SSD is long, even in the coherent field, we could confirm a pole-line around the theoretical value.
Phase response of transfer functions and coherent field in a reverberation room
This paper analyzes the properties of sound field transfer functions that change with the sound source distance (SSD), by measuring reverberant room impulse responses from a point of view of the phase characteristics. We analyzed the propagation phase (PP) according to the SSD in a reverberant field that R. Lyon investigated, by using a narrow-band linear regression analysis of the impulse responses and considered the relation to the zero distribution of the transfer function. As a result, we clarified that the SSD information is included in the phase frequency characteristics of the minimum-phase component and the variances from the PP. The distance from the source where the PP could be observed corresponds to the coherent field based on the wave theory or the critical distance defined by the energy ratio of direct to reverberation sound. Therefore, the field where the PP could be observed in the minimum-phase component of the transfer function can be treated as the direct sound field. In addition, we also present that the reverberation phase (RP) separated and extracted along with PP from the phase frequency characteristics is according to the estimated value from the number of non-minimum-phase zeros. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(4): 1–8, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20293
Conserved Quantities of a Class of Nonlinear Difference-Difference Equations
Higher-order conserved quantities of a class of nonlinear difference-difference equations which are related to the discrete-time Toda equation are obtained using the Miura transformations.