Block Diagram Interpretation of Time-Varying STFT Modifications

Assuming is causal gives

This is depicted in Fig.8.19.

The term can be interpreted as the FIR filter tap at time . Note how each tap is lowpass filtered by the FFT window . The window thus enforces bandlimiting of the filter taps the main lobe. For an -term length- Blackman-Harris window, for example, the main lobe reaches zero at frequency (see Table 1.2 in §1.7 for other examples). See Allen and Rabiner 1977 [10] for further details on the bandlimiting property.

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written by 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.