Spectrograms

The spectrogram is a basic tool in audio spectral analysis and other fields. It has been applied extensively in speech analysis [16]. The spectrogram can be defined as an intensity plot (usually on a log scale, such as dB) of the Short-Time Fourier Transform (STFT) magnitude. The STFT is simply a sequence of FFTs of windowed data segments, where the windows are usually allowed to overlap in time, typically by 25-50% [3]. It is an important representation of audio data because human hearing is based on a kind of real-time spectrogram encoded by the cochlea of the inner ear [47]. The spectrogram has been used extensively in the field of computer music as a guide during the development of sound synthesis algorithms. When working with an appropriate synthesis model, matching the spectrogram often corresponds to matching the sound extremely well. In fact, spectral modeling synthesis (SMS) is based on synthesizing the short-time spectrum directly by some means [83].

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Subsections

• Spectrogram of Speech

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Order a Hardcopy of Mathematics of the DFT

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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.