Abstract
In this paper, we report application procedures and observed results of multi-resolution Fourier analysis proposed in the first part of this series. Missing signal recovery derived from multi-resolution theory is developed. It is shown that multi-resolution Fourier analysis enhances dramatically performances of Fourier spectra suffering limitations traced to implicit time windowing. Observed frequency resolutions, improvement of frequency estimations, contraction of spectral leakage and recovery of missing parts of finite duration signals are in accordance with theoretical predictions.
Highlights
In the first part of this series [1], we proposed multi-resolution Fourier analysis of finite duration signals
Improvement of frequency estimations, contraction of spectral leakage and recovery of missing parts of finite duration signals are in accordance with theoretical predictions
In order to test resolution capabilities of described multi-resolution signals, let us consider a real signal composed of twoequi-power sinusoids of respective frequencies f0 and f1 observed in the constant time interval T and defined by
Summary
In the first part of this series [1], we proposed multi-resolution Fourier analysis of finite duration signals. Derived expression of multiresolution signals shows that the number of resolution levels are defined by increasing or decreasing the length of multi-resolution signals in order to depict respectively detailed or global views. In this second part, we report application procedures of multi-resolution signals and missing signal recovery. Reported observations are in accordance with theoretical predictions [1]
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