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Magnitude-only Analysis/Synthesis

A traditional result of sound perception is that the ear is sensitive principally to the short-time spectral magnitude and not to the phase, provided phase continuity is maintained. Our experience has been that this may or may not be true depending on the application, and in §H.0.9 we will discuss it. Obviously if the phase information is discarded, the analysis, the modification, and the resynthesis processes are simplified enormously. Thus we will use the magnitude-only option of the program whenever the application allows it.

In the peak detection process we calculate the magnitude and phase of each peak by using the complex spectrum. Once we decide to discard the phase information there is no need for complex spectra and we simply can calculate the magnitude of the peak by doing the parabolic interpolation directly on the log magnitude spectrum.

The synthesis also becomes easier; there is no need for a cubic function to interpolate the instantaneous phase. The phase will be a function of the instantaneous frequency and the only condition is phase continuity at the frame boundaries. Therefore, the frequency can be linearly interpolated from frame to frame, like the amplitude. Without phase matching the synthesized waveform will look very different from the original (Fig.H.5), but the sound quality for many applications will be perceptually the same.

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2016-07-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University