Combination of complex rectangular transforms and f.n.t. to implement fast convolution

Recently, complex rectangular transforms (c.x.r.t.s) have been derived which can be shown to be more efficient than rectangular transforms (r.t.s) for computing convolution of complex sequences. This letter proposes the combination of complex rectangular transforms with the Fermat number transform (f.n.t.) to devise efficient algorithms for computing error-free convolutions of both real and complex sequences. The results show that the combination of c.x.r.t. and f.n.t. requires fewer multiplications compared to that of r.t. and f.n.t.