The even subgroup of the Weyl group associated with the crystallographic root system \(A_1 \times A_1\) induces two-variable even Weyl orbit functions which form the kernels of the developed discrete Fourier–Weyl transforms. The finite point and label sets of the discrete trigonometric transforms are formed by rectangular fragments of the \(A_1 \times A_1\) admissibly shifted weight lattices in the Euclidean plane. Sixteen types of the point and label sets are listed and the related discrete orthogonality relations of the even Weyl orbit functions are demonstrated. The forward and backward transforms together with the linked interpolation formulas and orthogonal transform matrices are presented and exemplified.

与晶体根系\(A_1 \times A_1\)相关的外尔群的偶数子群产生二变量偶数外尔轨道函数，这些函数形成了离散傅里叶-外尔变换的核心。离散三角变换的有限点和标签集由欧几里得平面中\(A_1 \times A_1\)允许移位权重格的矩形片段形成。列出了十六种类型的点集和标签集，并证明了偶Weyl轨道函数的相关离散正交关系。给出并举例说明了前向和后向变换以及链接的插值公式和正交变换矩阵。