Chirplet Synthesis

An extension of IFFT synthesis to support linear frequency sweeps was devised by Michael Goodwin [90]. The basic idea was to tabulate window main-lobes for a variety of sweep rates. (The phase variation across the main lobe determines the frequency variation over time, and the width of the main lobe determines its extent.) In this way, frequencies could be swept within a FFT frame instead of having to be constant with a cross-fade from one static frame to the next.

Independently, Marques and Almeida introduced chirplet modeling of speech in 1989 [155]. This technique is based on the interesting mathematical fact that the Fourier transform of a Gaussian-windowed chirp remains a Gaussian pulse in the frequency domain. Instead of measuring only amplitude and phase at each a spectral peak, the parameters of a complex Gaussian are fit to each peak. The (complex) parameters of each Gaussian peak in the spectral model determine a Gaussian amplitude-envelope and a linear chirp rate in the time domain. Thus, both cross-fading and frequency sweeping are handled automatically by the spectral model. A specific method for carrying this out is described in §9.10.

More recent references on chirplet modeling include [186,88,89,87].

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.