On Properties, Relations, and Simplified Implementation of Filter Banks in the Dolby Digital (Plus) AC-3 Audio Coding Standards

The Dolby Digital (Plus) AC-3 audio coding standards are currently the key enabling technologies for high-quality compression and decompression of digital audio signals. The Dolby Digital (Plus) AC-3 audio coding standards have adopted the modified discrete cosine transform (MDCT) for the time/frequency transformation of an audio data block. Besides a long transform being the MDCT, the AC-3 defines additional two variants of cosine-modulated filter banks called the first and second short transforms. Based on the matrix representation of AC-3 filter banks, by a systematic investigation of their properties and relations among transform matrices, a relation between the frequency coefficients of the long (MDCT) and those of two short transforms is derived. Frequency coefficients of two short transforms in AC-3 can be simply obtained from the given frequency coefficients of the long (MDCT) transform via a conversion matrix. Since the conversion matrix after proper scaling is an orthonormal matrix with very regular general structure, the frequency coefficients of the short transforms can be converted to the frequency coefficients of the long (MDCT) transform via the transposed conversion matrix. Consequently, the current implementation of AC-3 filter banks for the time/frequency transformation of an audio data block can be simplified in the encoder and the forward long (MDCT) transform computation is required only. Further, it is shown that there exists a simple relation between the time domain aliased data sequence recovered by the backward long (MDCT) and those of two short transforms. Consequently, the current implementation of AC-3 filter banks can be also simplified in the decoder and the backward long (MDCT) transform computation is required only. Thus, the computation of two short transforms in both the AC-3 encoder and decoder can be completely eliminated. Moreover, due to the existence of both relations between transform coefficients and time domain aliased data sequences, the conversion matrix in the AC-3 encoder and decoder may not be used at all.