On Vibrato and Frequency (De)Modulation in Musical Sounds
Vibrato is an important characteristic in human musical performance and is often uniquely characteristic to a player and/or a particular instrument. This work is motivated by the assumption (often made in the source separation literature) that vibrato aids in the identification of multiple sound sources playing in unison. It follows that its removal, the focus herein, may contribute to a more blended combination. In signals, vibrato is often modeled as an oscillatory deviation from a center pitch/frequency that presents in the sound as phase/frequency modulation. While vibrato implementation using a time-varying delay line is well known, using a delay line for its removal is less so. In this work we focus on (de)modulation of vibrato in a signal by first showing the relationship between modulation and corresponding demodulation delay functions and then suggest a solution for increased vibrato removal in the latter by ensuring sideband attenuation below the threshold of audibility. Two known methods for estimating the instantaneous frequency/phase are used to construct delay functions from both contrived and musical examples so that vibrato removal may be evaluated.