The Short-Time Fourier Transform (STFT) and Time-Frequency Displays

Often we simply want to display sound as a spectrum that evolves through time. We know that this is what the brain ``sees'' when we hear sound. The classic spectrogram, developed at Bell Telephone Laboratories during World War II, has been used for decades to display the short-time spectrum of sound. There are even people who can ``read'' a spectrogram of speech. In Chapter 6, the classic spectrogram is reviewed, and development of more refined ``loudness spectrograms'' based on recent psychoacoustic research in loudness perception are discussed. These more refined spectrograms come closer to goal of ``what you see is what you hear''.

Since the proliferation of digital computers, spectrograms have been computed using the Short-Time Fourier Transform (STFT), which is simply a sequence of FFTs over time. In Chapter 6, the STFT is introduced.

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About the Author: 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.