Windowed Fourier phase: completeness and signal reconstruction

It is established that a signal, either continuous or discrete, is determined up to a multiplicative constant by its windowed Fourier phase (WFP) at any frequency. This result indicates that the WFP contains richer information than zero crossings and peaks. It also provides insight into why WFP-based image matching may achieve highly accurate and stable results. To experimentally demonstrate the completeness of the WFP, an algorithm is developed to reconstruct signals from the WFP.<
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