Improved radix-3 decimation-in-frequency algorithm for the fast computation of forward and inverse MDCT

Shu et al. recently proposed an efficient radix-3 decimation-in-Frequency (DIF) algorithm for the fast computation of forward and inverse modified discrete cosine transform (MDCT). Their algorithm decomposes the MDCT of a sequence with length N = 2×3^m and the IMDCT of a sequence with length N = 4×3^m into three N/3-point MDCTs and IMDCTs, respectively. In this paper, we present a refinement of their approach. Comparison with Shu´s algorithm shows that the number of arithmetic operations can be reduced from 17.5% to 20.5% for MDCT and from 23.1% to 27.9% for IMDCT when N is varying from 36 to 324.