New universal rotation-based fast computational structures for an efficient implementation of the DCT-IV/DST-IV and analysis/synthesis MDCT/MDST filter banks

New universal rotation-based fast computational structures identical both for the discrete cosine/sine transform of type IV (DCT-IV/DST-IV) and the forward/backward modified discrete cosine/sine transform (MDCT/MDST) computation are described. They are the result of a systematic construction of a fast algorithm for an efficient implementation of the time domain aliasing cancellation (TDAC) analysis/synthesis MDCT/MDST filter banks employed in various audio compression schemes. New fast algorithms provide novelty computational structures based exclusively on the computation of Givens–Jacobi rotations, and thus, the need of any discrete sinusoidal unitary transform such as the discrete Fourier transform (DFT), DCT-IV/DST-IV or discrete cosine/sine transforms of type II (DCT-II/DST-II) of reduced size is completely eliminated, so simplifying the computational structure of the algorithms. The rotators and summators are used only as the basic computational modules (in a hardware implementation they are simple hardware blocks). The simple and regular Givens–Jacobi rotation-based fast computational structures valid for any N divisible by 4 (N   being the length of data sequence) define new sparse matrix factorizations of the DCT-IV and MDCT matrices and in particular, generate an efficient implementation of the MDCT in MP3 audio coding standard. For a given N=2nN=2n they can be easily reconfigurable for a specific audio coding scheme. Finally, since Givens–Jacobi rotation can be factored into a product of Gauss elementary matrices being unit lower and unit upper triangular matrices, the new fast rotation-based computational structures are suitable for an integer approximation of the DCT-IV/DST-IV (integer DCT-IV/DST-IV) and MDCT/MDST (integer MDCT/MDST) which are currently modern transform technologies for lossless audio coding.