用实数卷积计算代数数域上整数卷积

ON THE CALCULATION OF INTEGER'S CYCLIC CONVOLUTION OVER ALGEBRAIC NUMBER FIELDS

在信息的数字处理中,卷积是最常见的一种,通常又是通过循环卷积来算.随着数论变换的兴起,人们逐渐用DFT的方法计算整数、复整数甚至代数整数的循环卷积.本文推广了文[2]的方法到一般代数数域上,得出相应的结果.最后证明了进一步的结果:复整数卷积可只通过一次普通卷积算出.

Sun Qi, Zheng Dexun and Shen Zhongqi discuss integer's cyclic convolutions over quadratic fields, cyclotomic fields and other algebraic mumber fields in [1], In[2] an arbitrary cyclic convolution over Z[i] is turned into two cyclic convolutions over Z.Applying its manner, we obtain some similiar results over algebraic number fields. At last we obtain a further result that an arbitrary cyclic convolution over Z[i] can be calculated by calculating one cyclic convolution over Z.