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

Area of Science:

• Acoustics and Signal Processing
• Bioengineering
• Physical Systems Analysis

Background:

• Causality in physical systems mandates one-sided time impulse responses.
• Reported two-sided impulse responses in ear-canal reflectance measurements synthesized via inverse discrete Fourier transform (IDFT) lack clear explanation.
• Negative-time components in these responses are often unclear in significance and origin.

Purpose of the Study:

• To clarify the sources of negative-time components in IDFT impulse responses.
• To illustrate the implications of enforcing one-sided impulse responses for aural systems.
• To explore the utility of two-sided impulse responses in practical applications.

Main Methods:

• Analysis of ideal and practical examples to identify sources of negative-time components.
• Investigation of the properties of the discrete Fourier transform (DFT) and IDFT in system analysis.
• Examination of frequency-domain measurements and their relation to time-domain impulse responses.

Main Results:

• Negative-time components in IDFT impulse responses arise from the two-sided nature of the DFT, particularly in frequency-domain measurements.
• Ideal and practical examples demonstrate the mechanisms leading to these two-sided responses.
• Constraining aural IDFT impulse responses to be one-sided has specific implications for system interpretation.

Conclusions:

• Two-sided IDFT impulse responses are a consequence of the DFT's properties when applied to physical system measurements.
• Despite appearing non-physical, two-sided impulse responses derived from ear-canal reflectance measurements can be practically and diagnostically valuable.