Ircam - Centre Georges-Pompidou

Infinite length windows for short-time Fourier transform

Analysis-synthesis team
IRCAM, Institut de Recherche et de Coordination Acoustique-Musique
1 place Igor-Stravinsky, 75004 PARIS, FRANCE



Short-time Fourier transform (STFT) is a widely-used signal processing tool for sound analysis and synthesis. It is commonly used, as an example, for time-frequency analysis as well as in the Phase Vocoder. Since only a finite number of operations is possible in a computer implementation of the STFT, in most cases the analysis and the synthesis window are of finite length, i.e. a FIR filter impulse response. Using such a finite impulse response as STFT analysis or synthesis window usually leads to a tradeoff between time resolution, frequency resolution and amplitude of side lobes. Different optimal windows have been developed for different problems: Hann windows, Hamming windows, Kaiser windows...

In this paper, we propose an algorithm for computing, in a finite number of operations, the STFT of a signal windowed by a rational infinite length window, i.e. by the impulse response of an ARMA filter. This work extends the STFT theory to infinite length windows. Notice, for instance, that the well-known gammatone filter used in psychoacoustic research is a typical infinite length window.

We present one particular achievement of this work concerning the problem of designing new optimized windows for specific analysis or synthesis problems. Infinite length windows do not follow the same constraints as do RIF filters. For instance, when designing optimal low pass filters, the criteria comprise minimizing the ripples, maximizing the slope, and the flatness of the transfer function. Therefore we present new window families, and some tradeoff criteria for the choice of windows adapted to various problems. In particular, the infinite window analysis is applied to the tracking of partials for additive sound synthesis. Results and performances of these windows are compared to those of usual methods. The pros and cons of this algorithm with regard to common STFT will be discussed for the tracking problem, but also for other problems such as sound modification with a Phase Vocoder.

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Tue May 12 13:14:48 1998
Tassart Stéphan

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