Linear canonical transforms (LCTs) are extensively used in many areas of science and engineering with many applications, which requires a satisfactory discrete implementation. Recently, hyperdifferential operators have been proposed as a novel way of defining the discrete LCT (DLCT). Here we first focus on improving the accuracy of this approach by considering alternative discrete coordinate multiplication and differentiation operations. We also consider canonical decompositions of LCTs and compare them with the originally proposed Iwasawa decomposition. We show that accuracy of the approximation of the continuous LCT with the DLCT can be drastically improved. The advantage and elegance of this approach lie in the fact that it reduces the problem of defining sophisticated discrete transforms to merely defining discrete coordinate multiplication and differentiation operations, by reducing the transforms to these operations. As a result of systematic investigation of possible parameters and design choices, we achieve a DLCT that is both theoretically satisfying and highly accurate.

线性规范变换 (LCT) 广泛用于科学和工程的许多领域，具有许多应用，这需要令人满意的离散实现。最近，已经提出了超微分算子作为定义离散 LCT (DLCT) 的一种新方法。在这里，我们首先通过考虑替代离散坐标乘法和微分运算来提高这种方法的准确性。我们还考虑了 LCT 的规范分解，并将它们与最初提出的 Iwasawa 分解进行了比较。我们表明，使用 DLCT 逼近连续 LCT 的准确性可以大大提高。这种方法的优点和优雅在于，它通过减少对这些操作的变换，将定义复杂离散变换的问题减少到仅定义离散坐标乘法和微分运算。作为对可能的参数和设计选择的系统研究的结果，我们实现了一个在理论上令人满意且高度准确的 DLCT。