Time-Frequency Displays

The preceding chapters have been concerned with the spectrum analysis
of sinusoids and noise at a particular point in time (or a single
spectrum for all time). This chapter introduces the *Short-Time
Fourier Transform* (STFT)--a time-ordered sequence of spectral
estimates, each using a finite-length analysis window. The STFT is
used to compute the classic *spectrogram*, used extensively for
*speech* and audio signals in general
[132,57,199,162,226,74,81].
Finally, we point to methods for making spectrograms correspond better
to *audio perception*, so that *what you see is what you
hear*, to a greater extent. In particular, a *loudness
spectrogram* based on a psychoacoustic model of time-varying loudness
perception is described.

- The Short-Time Fourier
Transform
- Mathematical Definition of the STFT
- Practical Computation of the STFT
- Summary of STFT Computation Using FFTs
- Two Dual Interpretations of the STFT
- The STFT as a Time-Frequency Distribution
- STFT in Matlab

- Classic Spectrograms

- Audio Spectrograms

- Summary

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University