A Sparsity Measure for Echo Density Growth in General Environments

We study the detailed temporal evolution of echo density in impulse responses for applications in acoustic analysis and rendering on general environments. For this purpose, we propose a smooth sorted density measure that yields an intuitive trend of echo density growth with time. This is fitted with a general power-law model motivated from theoretical considerations. We validate the framework against theory on simple room geometries and present experiments on measured and numerically simulated impulse responses in complex scenes. Our results show that the growth power of echo density is a promising statistical parameter that shows noticeable, consistent differences between indoor and outdoor responses, meriting further study.