Time-Frequency Parameters in the STFT

The basic STFT parameters control the following time-frequency properties:

• The window length determines the time and frequency resolution of the STFT. In general, frequency resolution is inversely proportional to time resolution. An example STFT time-frequency tiling is shown in Fig.8.16.

• In the DFT, the time-frequency resolution is uniform, i.e., frequency bins are linearly spaced, and data frames are uniformly spaced in time, as shown in Fig.8.16. In Chapter 11, we will look also at the ``constant-Q'' time-frequency tiling, which is closer to audio perception than the rectangular tiling of the STFT.

• The FFT length determines
  • the degree of spectral interpolation, and
  • the degree of spectral modifications which are possible without time aliasing.
  The FFT length minus the data window length, , gives the amount of zero-padding we are using for spectral interpolation. Only oversampled (interpolated) spectra can be modified multiplicatively without causing time aliasing.

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Order a Hardcopy of Spectral Audio Signal Processing

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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.