Time and frequency representations are linked so short durations broaden bandwidth

Evidence

Because psychoacoustics is concerned with measuring the limits of auditory perception on various acoustic dimensions, understanding the waveform and spectral representation of sound is important. The waveform, which plots amplitude versus time, contrasts with the spectrum, which plots amplitude versus frequency. The waveform can only be represented using instantaneous amplitude, but the spectrum typically uses a decibel metric. However, the two representations are two sides of the same coin, so shortening the duration of the stimulus will concomitantly lead to a broadening of the bandwidth of the stimulus. — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 209

Categorization

• DEFINE: The time-bandwidth reciprocity (uncertainty relation) stated in accessible terms — foundational for understanding masking and frequency resolution in impaired hearing.
• QUESTION: Worth chasing later: this uncertainty tradeoff underpins how hearing-impaired listeners’ reduced frequency resolution interacts with temporal cues — an application angle.