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Uncertainty principles associated with quaternionic linear canonical transforms. (English) Zbl 1407.94037

Summary: In the present paper, we generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic LCT (QLCT). Using the properties of the LCT, we establish an uncertainty principle for the two-sided QLCT. 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 quaternionic signal minimizes the uncertainty.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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