Recursive architectures for the forward and inverse modified discrete cosine transforms

This paper presents recursive architectures for the modified discrete cosine transform (MDCT) and its inverse transform (IMDCT) which are the most complex operations in layer 3 of the MPEG audio coding standard. By rearranging the input data, we first derive two trigonometric equations, which can be represented as the Chebyshev polynomials. Then we demonstrate that the general length of MDCT and IMDCT can be efficiently implemented by the recursive structure. The computational complexity of each data throughput in these two architectures is less than existing related systems by as many as 50%. The proposed regular structure is particularly suitable for parallel VLSI realization.