A higher order method for concentrating the STFT

D. J. Nelson, D. C. Smith

Research output: Contribution to journalConference articlepeer-review

4 Scopus citations


We present a method for computing the theoretically exact estimate of the instantaneous frequency of a signal from local values of its short time Fourier transform under the assumption that the complex logarithm of the signal is a polynomial in time. We apply the method to the problem of estimating and separating non-stationary components of a multi-component signal. Signal estimation and separation is based on a linear TF model in which the value of the signal at each time is distributed in frequency. This is a significant departure from the conventional nonlinear model in which signal energy is distributed in time and frequency. We further demonstrate by a simple example that IF estimated by the higher order method is significantly better than previously used first order methods.

Original languageEnglish
Article number59100G
Pages (from-to)1-8
Number of pages8
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2005
Externally publishedYes
EventAdvanced Signal Processing Algorithms, Architectures, and Implementations XV - San Diego, CA, United States
Duration: Aug 2 2005Aug 4 2005


  • Adaptive filter
  • Energy distributions
  • Interference removal
  • Linear TF distributions
  • Linearity
  • Marginals
  • Short time fourier transform
  • Spectrogram
  • Wigner distribution


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