Instantaneous frequency decomposition: an application to spectrally sparse sounds with fast frequency modulations.
Classical time-frequency analysis is based on the amplitude responses of bandpass filters, discarding phase information. Instantaneous frequency analysis, in contrast, is based on the derivatives of these phases. This method of frequency calculation is of interest for its high precision and for reasons of similarity to cochlear encoding of sound. This article describes a methodology for high resolution analysis of sparse sounds, based on instantaneous frequencies. In this method, a comparison between tonotopic and instantaneous frequency information is introduced to select filter positions that are well matched to the signal. Second, a cross-check that compares frequency estimates from neighboring channels is used to optimize filter bandwidth, and to signal the quality of the analysis. These cross-checks lead to an optimal time-frequency representation without requiring any prior information about the signal. When applied to a signal that is sufficiently sparse, the method decomposes the signal into separate time-frequency contours that are tracked with high precision. Alternatively, if the signal is spectrally too dense, neighboring channels generate inconsistent estimates-a feature that allows the method to assess its own validity in particular contexts. Similar optimization principles may be present in cochlear encoding.
Gardner
T J
TJ
Laboratory of Mathematical Physics, The Rockefeller University, 1230 York Ave, New York, New York 10021, USA. tgardner@mit.edu
Magnasco
M O
MO
D000162:Acoustics / Q000295:instrumentation*; D006801:Humans; D008962:Models, Theoretical; D013016:Sound; D013018:Sound Spectrography; D014831:Voice