【摘 要】
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The quaternion Fourier transform-a generalized form of the classical Fourier transform-has been shown to be a powerful analyzing tool in image and signal pr
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The quaternion Fourier transform-a generalized form of the classical Fourier transform-has been shown to be a powerful analyzing tool in image and signal processing.This paper investigates the Pitts inequality and uncertainty principle associated with the two-sided quaternion Fourier transform.It is shown that by applying the symmetric form $f=f_1 + {\bf i}\,f_2 + f_3\,{\bf j} + {\bf i}\,f_4\,{\bf j}$ of quaternion from Hitzer and the novel module or $L^p$-norm of the quaternion Fourier transform $\widehat f$,then any nonzero quaternion signal and its quaternion Fourier transform cannot both be highly concentrated.Two part results are provided,one part is the Heisenberg-Weyls uncertainty principle associated with the quaternion Fourier transform.It is formulated by using logarithmic estimates which may obtained from a sharp of Pitts inequality; the other part is the uncertainty principle of Donoho and Stark associated with the quaternion Fourier transform.
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