  In this paper, we offer and discuss three efficient structural solutions for
the hardware-oriented implementation of discrete quaternion Fourier transform
basic operations with reduced implementation complexities. The first solution:
a scheme for calculating sq product, the second solution: a scheme for
calculating qt product, and the third solution: a scheme for calculating sqt
product, where s is a so-called i-quaternion, t is an j-quaternion, and q is an
usual quaternion. The direct multiplication of two usual quaternions requires
16 real multiplications (or two-operand multipliers in the case of fully
parallel hardware implementation) and 12 real additions (or binary adders). At
the same time, our solutions allow to design the computation units, which
consume only 6 multipliers plus 6 two input adders for implementation of sq or
qt basic operations and 9 binary multipliers plus 6 two-input adders and 4
four-input adders for implementation of sqt basic operation.
