Abstract
The reassignment method is a non-linear, post-processing technique which cans improve the localization of a time-frequency distribution by moving its values according to a suitable vector field. The reassignment method’s scheme assumes that the energy distribution in the time-frequency plane resembles a mass distribution and moves each value of the time-frequency plane located at a point (풕풕,풇풇) to another point,(풕풕�,풇풇�), which is the center of gravity of the energy distribution in the area of (풕풕,풇풇). The result is a focused representation with very high intensity [11]. During this research it was investigated and determined that the frequency reassignment corrections derived from the Flandrin reassignment method have undesired noise sensitivity at very small noise levels as well as undesired observed distortions. In order to address these issues, a novel approach was derived - the discrete-time, discrete-frequency formulation of frequency reassignment. It is shown that in noise-free tone scenarios, this novel approach eliminates ambiguity and provides less distortion than the Flandrin reassignment method.
Highlights
The reassignment method is a post-processing technique aimed at improving the readability of timedistribution in the area of
Reassignment method was many years later when several papers were written by Auger and Flandrin [2], [4] in which reassignment equations were derived for the spectrogram, and for a number of other time-frequency and time-scale distributions
The value of the resulting modified time- readability that the reassignment method provides over scale representation on any point is the sum its classical time-frequency distribution counterpart
Summary
Reassigned spectrograms are very new distribution is that it uses the phase easy to implement, and do not require a drastic increase information of the STFT, and its squared in computational complexity. Where Φxx (tt, ff; h) is the phase of the STFT of xx : Φxx (tt, ff; h) = arg FFxx(t, f; h)) These expressions (equations (5) and (6)) do not lead to an efficient implementation, and have to be replaced by equations (7) (local group delay) and (8) (local instantaneous frequency): coefficients, it is no longer available for use in reconstruction. TTh (tt) tt × h(tt) and DDh (tt) ddh ddtt (tt) This leads to an efficient implementation for the reassigned spectrogram without explicitly computing the partial derivatives of phase. The value of the resulting modified time- readability that the reassignment method provides over scale representation on any point (tt′ , aa′ ) is the sum its classical time-frequency distribution counterpart.
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