Untangling Phase and Time in Monophonic Sounds

TL;DR

This paper introduces a mathematical model for monophonic sounds that independently manipulates phase and time, enabling advanced sound resynthesis, pitch shifting, and creative effects with an efficient streaming algorithm.

Contribution

The paper proposes a novel model that separates phase and time in monophonic sounds, fulfilling natural properties and enabling versatile sound processing techniques.

Findings

Model exactly fulfills natural properties like time-invariance and envelope preservation.

Efficient algorithm implemented in Haskell for real-time processing.

Supports applications like pitch shifting, FM synthesis, and ultrasound audibility.

Abstract

We are looking for a mathematical model of monophonic sounds with independent time and phase dimensions. With such a model we can resynthesise a sound with arbitrarily modulated frequency and progress of the timbre. We propose such a model and show that it exactly fulfils some natural properties, like a kind of time-invariance, robustness against non-harmonic frequencies, envelope preservation, and inclusion of plain resampling as a special case. The resulting algorithm is efficient and allows to process data in a streaming manner with phase and shape modulation at sample rate, what we demonstrate with an implementation in the functional language Haskell. It allows a wide range of applications, namely pitch shifting and time scaling, creative FM synthesis effects, compression of monophonic sounds, generating loops for sampled sounds, synthesise sounds similar to wavetable synthesis, or making ultrasound audible.