Complex rectangular transforms for digital convolution

Agarwal and Cooley have presented "rectangular transforms" for cyclic convolution, which are derived with the aid of the Chinese Remainder Theorem and factorization of the polynomial (z
^N
- 1) into irreducible polynomials. The set of polynomials used by Agarwal and Cooley has coefficients from the field of real integers. The authors [3] have considered the set of polynomials with complex integer coefficients and derived new algorithms, referred to as "complex rectangular transforms," In this correspondence we present the detailed algorithms and show that, in many cases, they require fewer arithmetic operations than rectangular transforms for convolution of complex sequences.