Time-Frequency Parameters in the STFT

Figure: Example time-frequency tiling for the STFT. Vertical line spacing indicates time resolution, and horizontal line spacing indicates frequency resolution (both fixed). The area of the rectangular cells are bounded below by the minimum time-bandwidth product (see §B.1.17 for one definition).

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

• The window length $M$ 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.7.16.

• 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.7.16. In Chapter 10, 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 $N$ 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, $N-M$ , gives the amount of zero-padding we are using for spectral interpolation. Only oversampled (interpolated) spectra can be modified multiplicatively without causing time aliasing.