On causality and aural impulse responses synthesized using the inverse discrete Fourier transform

Causality is a fundamental property of physical systems and dictates that a time impulse response characterizing any causal system must be one-sided. However, when synthesized using the inverse discrete Fourier transform (IDFT) of a corresponding band-limited numerical frequency transfer function, several papers have reported two-sided IDFT impulse responses of ear-canal reflectance and ear-probe source parameters. Judging from the literature on ear-canal reflectance, the significance and source of these seemingly non-physical negative-time components appear largely unclear. This paper summarizes and clarifies different sources of negative-time components through ideal and practical examples and illustrates the implications of constraining aural IDFT impulse responses to be one-sided. Two-sided IDFT impulse responses, derived from frequency-domain measurements of physical systems, normally occur due to the two-sided properties of the discrete Fourier transform. Still, reflectance IDFT impulse responses may serve a number of practical and diagnostic purposes.