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Sines+Noise+Transients Time-Frequency Maps

Figure 10.13 shows the multiresolution time-frequency map used in the original S+N+T system [149]. (Recall the fixed-resolution STFT time-frequency map in Fig.7.1.) Vertical line spacing in the time-frequency map indicates the time resolution of the underlying multiresolution STFT,11.11 and the horizontal line spacing indicates its frequency resolution. The time waveform appears below the time-frequency map. For transients, an interval of data including the transient is simply encoded using MPEG-2 AAC. The transient-time in Fig.10.13 extends from approximately 47 to 115 ms. (This interval can be tighter, as discussed further below.) Between transients, the signal model consists of sines+noise below 5 kHz and amplitude-modulated noise above. The spectrum from 0 to 5 kHz is divided into three octaves (``multiresolution sinusoidal modeling''). The time step-size varies from 25 ms in the low-frequency band (where the frequency resolution is highest), down to 6 ms in the third octave (where frequency resolution is four times lower). In the 0-5 kHz band, sines+noise modeling is carried out. Above 5 kHz, noise substitution is performed, as discussed further below.

Figure 10.13: S+N+T Time-Frequency Map (from [149]).

Figure 10.14 shows a similar map in which the transient interval depends on frequency. This enables a tighter interval enclosing the transient, and follows audio perception more closely (see Appendix E).

Figure 10.14: Quasi-Constant-Q (Wavelet) Time-Frequency Map [149].

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University