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Theorem 2.1 (First convolution theorem of HHT).
This is the fractional circular convolution theorem.
Local asymptotic normality is established and applied to prove Hájek's convolution theorem for this functional.
Then, we derive a convolution theorem for discrete time signal in discrete time FRFT (DTFRFT) domain.
The obvious choice is the proof of the convolution theorem.
We then establish a certain convolution theorem for the HHT.
The convolution theorem in FT domain is shown to be a special case of our achieved results.
The conventional convolution theorem in FT domain is shown to be special cases of our achieved results.
The convolution theorem for the linear canonical transform (LCT) is of importance in signal processing theory and application.
Last, as an application, utilizing the new convolution theorem, we investigate the multiplicative filter in the SAFT domain.
This algorithm is based in the convolution theorem and it uses only two FFT calculi.
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