Envelope and fine structure cues are mathematically separable but perceptually entangled

Evidence

Numerous works about pitch perception attempt to identify and to distinguish between relevant temporal cues as envelope and fine structure. These cues are generally viewed as independent. In fact, mathematically, these cues are orthogonal and can be extracted and separated using a Hilbert transform. Using this mathematical decomposition, some works suggest that musical pitch would rely mostly on the fine structure and that speech perception would rely mostly on envelope (Smith et al. 2002 ). To empirically distinguish between envelope and fine structure cues in pitch perception experiments, a dedicated signal has been proposed as early as 1956 (De Boer 1956 ). This signal is equivalent of an unresolved harmonic complex tone with all harmonics shifted by the same amount of Hz. As the frequency distance between adjacent components of such a signal is regular and identical than in the original harmonic complex tone, such a signal has the same envelope but a different fine structure. As a consequence, any perceptual difference between the harmonic and the shifted complex is often interpreted as a pure fine structure based percept. — Dijk, Pim van, Physiology, Psychoacoustics and…, 4615

Categorization

• DEFINE: Explains the Hilbert-transform orthogonality of envelope and fine structure, and the De Boer (1956) shifted-complex signal that dissociates them.