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.
Progressive phase trends in multi‐degree‐of‐freedom systems
The relative phase of the response of a dynamical system to its excitation has been largely ignored in problems dealing with noise response of such systems. This is because mean‐square amplitude functions are able to predict many of the quantitites that one is interested in such as crack growth, noise radiation, and clearance impact probabilities without concern for phase. But phase has an essential role in other cases, such as phase coherence of vibration fields, or the design of filters to ‘‘dereverberate’’ a received signal. This paper describes some early results of the analysis of phase response of multi‐degree‐of‐freedom systems, using ideas that are closely related to statistical energy analysis, until now, used exclusively for the kinds of problems listed above that tend to ignore phase. The present results show good agreement between simple theory and experiments, but more importantly, they suggest directions for further work that should have significant payoff in the future.
Transfer function phase and truncated impulse response
Transfer function (TF) phase can be analyzed from the impulse response in a vibrating system. This letter analyzes the truncated impulse response of such a system and its phase characteristic by using a simple two‐pole model. The estimated phase turns out to be highly sensitive to the window length of the truncated impulse response used for phase analysis. The minimum‐phase behavior of a TF for example, is changed into a nonminimum‐phase characteristic due to the truncation. An exponential window is recommended for the data analysis of vibrating systems in order to reduce the effect of truncation on the phase.