Fast and Efficient Computation of MDCT/IMDCT Algorithms for MP3 Applications

The modified discrete cosine transforms (MDCT) and its inverse (IMDCT) has become important for audio codec. MDCT/IMDCT algorithms are widely applied to realize the analysis/synthesis filter banks of the time-domain aliasing cancellation scheme for sub band coding in various audio standards. The inverse modified discrete cosine transform (IMDCT) is the most computational intensive operations in the MPEG audio decoding standard. Efficient algorithms for realizing the IMDCT become very important in decoding process. This paper presents a novel and efficient algorithm for computation of Inverse modified Discrete Cosine Transform (IMDCT) with block size N=12 and 36 points is proposed based on type IV DCT and type II DCT, which improves the efficiency of computation. Firstly IMDCT with block size N is converted into type IV DCT, which is further transformed into DCT II with block size N/4. Comparison of the computational complexity with some known algorithms shows that the proposed new approach reduces the number of arithmetic operations significantly such as number Multiplications and Additions.