Sampling for Quaternion Bandlimited Signals in the Offset Linear Canonical Transform Domains

ABSTRACT The paper mainly studies the uniform sampling problems of quaternion bandlimited signals in the two‐dimensional offset linear canonical transform domains. Based on the systematic analysis for the sampling theory of quaternion bandlimited signals in the Fourier transform domains, we establish the sampling theorems for quaternion bandlimited signals in the offset linear canonical transform domains, where the imaginary units used in defining the transforms are different from those in the quaternion representation. The results show that the sampling formulas have essential differences for the three kinds of transforms, even though the bandlimited rectangular is symmetric about the origin. Moreover, numerical simulations demonstrate the efficiency of the proposed sampling theorems.