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An uncertainty principle for quaternion Fourier transform. (English) Zbl 1165.42310
Summary: We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty.
MSC:
42C15General harmonic expansions, frames
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