Diagnosing scattering with the Wigner distribution
James B. Lee · The Journal of the Acoustical Society of America · 2005
The Wigner distribution resolves the power of a signal in both the time domain and the frequency domain. It also is a complete representation because it displays the relative phases of a signal’s components as cross-products between them. This means that if one records the time-series of an impulse response in a room and computes a Wigner distribution from it, the kind of scattering, predominantly resonant or predominantly specular, is readily apparent, because the phase response of each is radically different. Specular scattering preserves the relative phases among components comprising the initial impulse and so preserves the impulse itself; resonant scattering randomizes the phases among components and so converts an impulse into a wide band of frequencies spread smoothly in time. Thus specular scattering tends to promote echoes and resonant scattering tends to promote diffusion. Graphic examples of each are given in the literature.