Complexity of waveform formulated from Fourier spectrum -- Theory and experiment

A new method of spectrum analysis for evaluating the diffuseness of sound fields is presented herein. We apply a concept of entropy, of complexity of waveform, to a Fourier transform of the signal. Thus, a measure of complexity in sound fields is defined as a complex entropy in terms of the frequency components of the complex Fourier transform. We theoretically and experimentally discuss the quantitative difference between two entropies, which is dependent on the distance between two measuring points in free sound and reverberant sound fields, excited by various signals. Computational procedures of signal processing are also described. It is found that this theory predicts the experimental values reasonably exactly in both sound fields. The entropy is considered to be useful for evaluating the diffuseness of sound fields, and to be appropriate for the field of room acoustics.