Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are extensively used to analyze and process multicomponent signals, i.e. superpositions of modulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relation inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the CWT, it provides a sharp, concentrated representation, while remaining invertible. This technique received a rened interest with the recent publication of an approximation result related to the application of the synchrosqueezing to multicomponent signals. In the current paper,  adapt the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework. The emphasis is put on the differences with the CWT-based synchrosqueezing with numerical experiments illustrating our statements.
['Thomas Oberlin', 'Sylvain Meignen', 'Valérie Perrier']
I am writing a research paper on a idea The fourier-based synchrosqueezing transform
[{"from": "human", "value": "I am writing a research paper on a idea The fourier-based synchrosqueezing transform"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are extensively used to analyze and process multicomponent signals, i.e. superpositions of modulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relation inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the CWT, it provides a sharp, concentrated representation, while remaining invertible. This technique received a rened interest with the recent publication of an approximation result related to the application of the synchrosqueezing to multicomponent signals. In the current paper,  adapt the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework. The emphasis is put on the differences with the CWT-based synchrosqueezing with numerical experiments illustrating our statements."}]