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In the present article, we first introduce the definition of the discrete double-sided quaternionic Fourier transform (DQFT) and obtain its inverse. We give examples how to compute the DQFT. We derive a discrete version of the duality property of the DQFT. We finally present an application of the DQFT to study the two-dimensional discrete linear time-varying systems.

Discrete Double-Sided Quaternionic Fourier Transform and Application