Inverse FFT Synthesis

When the number of partials is large, an explicit oscillator bank requires a significant amount of computation, and it becomes more efficient to use the inverse FFT to synthesize large ensembles of sinusoids [34,225,135,134,132]. This method gives the added advantage of allowing non-sinusoidal components such as filtered noise to be added in the frequency domain [228,231].

Inverse-FFT (IFFT) synthesis was apparently introduced by Hal Chamberlin in his classic 1980 book ``Musical Applications of Microprocessors'' [34]. His early method consisted of simply setting individual FFT bins to the desired amplitude and phase, so that the inverse FFT would efficiently synthesize a sum of fixed-amplitude, fixed-frequency sinusoids in the time domain.

This idea was extended by Rodet and Depalle [225] to include shaped amplitudes in the time domain. Instead of writing isolated FFT bins, they wrote entire main lobes into the buffer, where the main lobes corresponded to the desired window shape in the time domain.^H.5 (Side lobes of the window transform were neglected.) They chose the triangular window ( main-lobe shape), thereby implementing a linear cross-fade from one frame to the next in the time domain.

A remaining drawback of IFFT synthesis was that the inverse FFT nominally synthesizes only sinusoids at a fixed frequency, so that a rapid glissando may become ``stair-cased'' in the resynthesis, stepping once in frequency per output frame.

---

Previous: Oscillator-Bank Resynthesis
Next: Chirplet Synthesis

Order a Hardcopy of Spectral Audio Signal Processing

---

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.