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 variabilities and zeros in a reverberant transfer function
The phase trend of a transfer function (TF) has a nearly constant group delay in a reverberant sound field under high modal overlap conditions. This phase trend is predictable from the number of nonminimum phase zeros of the TF. This paper investigates the phase variability from such a phase trend in a reverberant TF. These phase fluctuations, which are generally due to random occurrences of both poles and zeros, can be expressed using the group delay, which is the first derivative of the accumulated phase. Theoretical analysis of the group delay implies that its fluctuations have a ‘‘1/f’’ type of spectrum and that the variance of the group delay is independent of the frequency band and decreases as the damping of the system increases. The results are confirmed by the power spectrum and correlation analysis using measured TF records. Accumulated phase variances are also investigated on the basis of the Δ statistic [F. Dyson and M. Mehta, ‘‘Statistical Theory of the Energy Levels of Complex Systems. IV,’’...
The Female Face of God in Auschwitz: A Jewish Feminist Theology of the Holocaust
Introduction 1. Reading Post-Holocaust Theology from a Feminist Perspective 2. The Hiding of God's Face in Auschwitz 3. Feminist Intimations of the Holy in Auschwitz 4. Face to Face (with God) in Auschwitz 5. A Mother/God in Auschwitz 6. The Redemption of God in Auschwitz 7. The Princess and the City of Death: A Feminist Maaseh, after Rabbi Nachman of Bratslav. Notes. Select Glossary of Hebrew and Yiddish Terms