为了使DCT变换能够通用，首先通过对DCT变换原理进行研究，发现了变换基系数的取值个数与阶数的关系，并结合余弦函数的性质对其进行了证明；然后以此为基础，提出了一种N(N=2^k , k>0，下同）阶整数DCT变换基的通用生成算法（该算法无需对相应的浮点基进行具体分析）；接着通过巧妙排列系数的序号，使得生成的中间多项式具有极强的规律性；最后设计了一个N位M进制数，用来实现N重循环，以穷举所有的可能解，并成功对任意N元多项式组进行了求解。实验结果表明，只要计算机的能力足够强大，应用此算法便可以发现任意N×N整数DCT变换的所有可用基。

The relationship between amounts of coefficients and order in radix is discovered through research of DCT principle and proven in combination with the nature of cosine function. On this basis, a generic generating algorithm for N-order (N=2^k, k>0, sic passim) integer DCT transform radix is presented, which we do not need to analyze floating radix corresponding to integer’s. Through rearrange variations of coefficient, the mid-polynomials are extremely regularity. The group of polynomials in arbitrary N-variable is resolved by designing a N-digits with M as radix implementing N-loops to exhaust all possible solutions. The experimental results show that the algorithm can find all available radix for arbitrary N×N integer DCT as long as the computing capacity is enough.