ABSTRACT
The spectral analysis techniques developed thus far represent powerful signal processing tools if one is not especially concerned with signal timing. Classical or modern spectral methods provide a complete and appropriate solution for waveforms that are stationary; that is, waveforms that do not change in their basic properties over the length of the analysis (strictly speaking, that do not change in their statistical properties). Yet many waveforms-particularly those of biological origin-are not stationary, and change substantially in their properties over time. For example, the EEG signal changes considerably depending on various internal states of the subject: i.e., meditation, sleep, eyes closed. Moreover, it is these changes with time that are often of primary interest. Fourier analysis provides a good description of the frequencies in a waveform, but not their timing. The Fourier transform “of a musical passage tells us what notes are played, but it is extremely different to figure out when they are played” (Hubbard, 1998). Such information must be embedded in the frequency spectrum since the Fourier transform is bilateral, and the musical passage can be uniquely reconstructed using the inverse Fourier transform. However, timing is encoded in the phase portion of the transform, and this encoding is difficult to interpret and recover. In the Fourier transform, specific events in time are distributed across all of the phase components. In essence, a local feature in time has been transformed into a global feature in phase.
