Poles and Zeros of Power Response and Driving Point Impedance of a Source in Rooms: Fid-Bau Portal

Poles and Zeros of Power Response and Driving Point Impedance of a Source in Rooms

Tohyama, Mikio

The power response of a point source for free field could be estimated according to the real part of driving point impedance even in a reverberant room within variances 1/2M, where M is a modal overlap of the sound field. The poles are interlaced with the zeros for the driving point impedance so that no accumulation phase might be rendered. The imaginary part makes the impedance function to be causal in the time domain. The driving point impedance could be extended into the transfer function from the standard of poles and zeros. This chapter presents examples of magnitude and phase responses in reverberant space from a perspective of poles and zeros for the transfer function. The micro-structure of the transfer functions, such as movements of zeros along the frequency domain, reveals the phase delay (propagation phase) in the coherent region due to the distance from the source. Deviation from the propagation phase, as the distance increases, might be due to the movements of zeros from upper- to lower-half plane in the complex frequency plane. Real parts of transfer functions may follow the sinc functions in the coherent region that imply sound pressure responses of a point source.