Estimates of the local Fourier spectrum at every point of a \(1\text {-D}\) time series of length N can be educed by the S-transform (ST) as a \(2\text {-D}\) complex time-frequency representation of dimension \(N\times N\) . The t-f amplitude and phase plots provide quantitative and visual information on local spectral content. However, the large storage and computational requirements, markedly worse with multidimensional data series, places significant limitations in the usage of the ST. All the information for the entire \(N\times N\) ST is in each one of the N voices of the ST, which could be termed as N-fold redundancy. The complete ST matrix can be recreated from any one of the voices of the ST. Three compaction and restoration schemes, with low computational requirements, are presented. Based on trade-off between visual information, computation time, and storage requirements, any of the three methods may be adopted for compaction and reconstruction.

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Compaction and Restoration of the S-Transform Based on N-Fold Redundancy

  • Subrat Kumar Acharya,
  • Pyari Mohan Pradhan,
  • Lalu Mansinha

摘要

Estimates of the local Fourier spectrum at every point of a \(1\text {-D}\) time series of length N can be educed by the S-transform (ST) as a \(2\text {-D}\) complex time-frequency representation of dimension \(N\times N\) . The t-f amplitude and phase plots provide quantitative and visual information on local spectral content. However, the large storage and computational requirements, markedly worse with multidimensional data series, places significant limitations in the usage of the ST. All the information for the entire \(N\times N\) ST is in each one of the N voices of the ST, which could be termed as N-fold redundancy. The complete ST matrix can be recreated from any one of the voices of the ST. Three compaction and restoration schemes, with low computational requirements, are presented. Based on trade-off between visual information, computation time, and storage requirements, any of the three methods may be adopted for compaction and reconstruction.