Methods and devices for performing a fast modified discrete cosine transform of an input sequence

摘要

An improved fast N-point MDCT process and encoder/decoder is disclosed. The N-point MDCT may be realized through an N/2-point DCT algorithm. The N/2 DCT transform matrix is directly factored and the factored DCT transform matrices are used to develop a set of equations for realizing the N-point MDCT coefficients from an input sequence. The factoring of the DCT transform matrix may include expressing the DCT transform as a multiplication of matrices and exploiting mirror images within the matrices. It may further include simplifying at least one of the matrices by eliminating a variable based on trigonometric identity