J. M. Clowning, “The Synthesis of Complex Audio Spectra by Means of Frequency Modulation,” Journal of the Audio Engineering Society, Vol. 21, No. 7, 1973, pp. 526-534.

has been cited by the following article:

• TITLE: Untangling Phase and Time in Monophonic Sounds

  AUTHORS: Henning Thielemann

  KEYWORDS: Pitch Shifting, Time Stretching, Wave Table Synthesis

  JOURNAL NAME: Journal of Signal and Information Processing, Vol.1 No.1, December 1, 2010

  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 timeinvariance, 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.