Envelope and temporal fine structure are mathematically orthogonal and independently extractable via Hilbert transform

Evidence

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

Category: Definitional Content

• DEFINE: Defines the Hilbert-transform orthogonality of envelope and fine structure, the core conceptual split in temporal pitch research.
• QUESTION: Is the Hilbert transform’s orthogonality actually a valid decomposition of how the auditory system processes sound, or just a mathematical convenience?

Related

• Envelope and fine structure cues are mathematically separable but perceptually entangled (similarity 0.97)
• Shifting harmonic components changes fine structure while keeping envelope identical (similarity 0.88)
• Envelope and fine structure are mathematically orthogonal but not perceptually independent (similarity 0.88)
• Harmonically shifted complex tones isolate fine structure cues while holding envelope constant (similarity 0.85)
• Envelope and temporal fine structure exist at three distinct processing levels (similarity 0.84)
• Fine structure alone does not determine pitch differences in complex tones sharing envelope frequency (similarity 0.84)
• Temporal envelope suffices for speech while fine structure carries pitch information (similarity 0.83)
• Hilbert decomposition splits sound into envelope and fine structure for controlled re-synthesis (similarity 0.83)
• Speech envelope representation relies on Hilbert transform derived analytic signals (similarity 0.81)
• Temporal fine structure is vital yet not perceived as a temporal event (similarity 0.81)
• Periodicity cues for pitch split into fine-structure, envelope, and interaction periodicities (similarity 0.81)
• Intelligible speech needs only a small fraction of its time-frequency units (similarity 0.80)
• Shifted complex tones cannot isolate pure temporal fine structure effects in pitch (similarity 0.79)
• Pitch percepts may only require encoding fine-structure peaks near envelope maxima (similarity 0.79)
• Shifting harmonic partials upward raises perceived pitch despite unchanged envelope modulation (similarity 0.79)