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Mixed-radix Algorithm for the Computation of Forward and Inverse MDCT
Jiasong Wu1, Huazhong Shu, Lotfi Senhadji
1LTSI, Laboratoire Traitement du Signal et de l'Image INSERM : U642 Université de Rennes I Campus de Beaulieu, 263 Avenue du Général Leclerc - CS 74205 - 35042 Rennes Cedex,FR.
IEEE Transactions on Circuits and Systems. I, Regular Papers : a Publication of the IEEE Circuits and Systems Society
|January 25, 2011
Summary
A new mixed-radix algorithm enhances Modified Discrete Cosine Transform (MDCT) and Inverse MDCT (IMDCT) computations for MPEG audio coding. This method offers improved efficiency and parallel implementation suitability for audio encoding and decoding.
Area of Science:
- Digital Signal Processing
- Audio Compression Technologies
Background:
- Modified Discrete Cosine Transform (MDCT) and Inverse MDCT (IMDCT) are computationally intensive core components of MPEG audio coding standards.
- Efficient algorithms for MDCT/IMDCT are crucial for optimizing audio encoding and decoding performance.
Purpose of the Study:
- To introduce a novel mixed-radix algorithm for accelerating MDCT and IMDCT computations.
- To enhance the efficiency and suitability of MDCT/IMDCT algorithms for parallel processing in audio standards.
Main Methods:
- The proposed algorithm decomposes an N-point MDCT into smaller MDCTs using recursive radix-2 (decimation in frequency) and radix-3 (decimation in time) strategies.
- The algorithm is represented as a sparse matrix factorization, enabling straightforward derivation of the corresponding IMDCT algorithm via matrix transposition.
- The method is extendable to multidimensional cases using the vector-radix approach.
Main Results:
- The new mixed-radix algorithm demonstrates significant computational efficiency for MDCT/IMDCT.
- The algorithm is particularly well-suited for parallel implementation, enhancing performance in Layer III of MPEG-1 and MPEG-2 audio encoding/decoding.
- The sparse matrix factorization provides a clear pathway for deriving the inverse transform.
Conclusions:
- The presented mixed-radix algorithm offers a more efficient approach to MDCT/IMDCT computations compared to existing methods.
- Its suitability for parallel implementation makes it a valuable advancement for real-time audio processing in MPEG standards.
- The algorithm's extensibility to multidimensional applications broadens its potential impact in signal processing.
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