New variation of Schroeder harmonic complex removes steady tones for cleaner auditory experiments

Alessandro Altoè (independent researcher) has published a preprint on arXiv introducing a refined version of the Schroeder harmonic complex, a periodic, band-limited signal used for decades to study how the auditory system perceives frequency modulation and dispersion. The original Schroeder complex sweeps in frequency over time, mimicking rising or falling tones. However, it also contains two steady, frequency-fixed components at its spectral edges. Because these components are easily audible to human listeners, they can confound behavioral experiments—subjects might respond to the steady tones rather than the intended sweep.

Altoè's variation suppresses these edge effects by adjusting the phase relationship of the harmonics, largely canceling the unwanted components while preserving the overall sweep-like structure. This simple but effective modification removes a long-standing artifact without altering the signal's core utility. The work has immediate implications for audiology and psychoacoustics research, where clean stimuli are critical for accurate measurements of frequency discrimination, modulation detection, and temporal processing. While the paper is academic, the technique could also find applications in audio processing and hearing aid algorithm testing.