16 September 2005 A higher order method for concentrating the STFT
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Abstract
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.
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D. J. Nelson, D. C. Smith, "A higher order method for concentrating the STFT", Proc. SPIE 5910, Advanced Signal Processing Algorithms, Architectures, and Implementations XV, 59100G (16 September 2005); doi: 10.1117/12.618153; https://doi.org/10.1117/12.618153
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