5.6 High Resolution Matching Pursuit

High Resolution Matching Pursuit  (HRMP) [GBM⁺96,GDR⁺96] is a method to decompose a sound into a time-frequency representation that keeps both the exact location in time of the fast transients (the attacks), and a good frequency resolution in the sustained parts. This matches the perceptive capabilities of the ear. Figure 4.3 shows an example.

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Since it is a time-frequency analysis, HRMP is not appropriate as such for spectral envelope representation, which pertains to one instance in time only, but it is an interesting method worth a look. The idea is to use a dictionary of primitive time-frequency components, called atoms, and to select the ones that together yield the closest match with the signal.

To apply HRMP to spectral envelope representation, it would be restricted to the frequency domain. The dictionary would contain curve pieces, especially formant shapes. Unfortunately this method would not be stable, since very different atoms could be selected for small changes. It would be local, because the atoms would have a small frequency support, and very flexible to manipulate. The easyness would depend on the dictionary used, as would the speed of synthesis and the space. (If the structures get too complex, significant redundancy could occur.)

HRMP structures would be very complicated to specify manually.