Fourier Transform Vs Wavelet Transform: Lipschitz Regularity of Functions

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Fourier transform is a strong tool for analyzing stationary functions. Whereas, wavelet transform is applicable to both stationary and non-stationary functions. However, Fourier transform does not achieve equivalence in the necessary and sufficient condition of Lipschitz regularity. On the contrary, the wavelet transform does, since wavelets are well localized
in time and frequency.

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