The Dolby Digital (AC-3) and the Dolby Digital Plus or Enhanced AC-3 (E-AC-3) systems are currently the key enabling technologies for high-quality compression of digital audio signals. For the time-to-frequency transformation of an audio data block and vice versa, both systems have adopted a long transform being the modified discrete cosine transform (MDCT). The AC-3 additionally defines two variants of cosine-modulated filter banks called the first and second short transforms. A fast conversion algorithm is presented to convert the frequency coefficients of the long (MDCT) transform to those of two short transforms and vice versa, directly in the frequency domain. It is based on a block sparse matrix factorization of a conversion matrix. The fast conversion algorithm is efficient in terms of the structural simplicity, arithmetic complexity and memory requirements compared to the obvious conversion methods. Moreover, the existing AC-3 fast computational modules may be simply re-used in the conversion procedures. Consequently, the E-AC-3 to AC-3 bit stream conversion and the AC-3 to E-AC-3 bit stream transcoding can be realized in a simplified and efficient way, thus minimizing the amount of partial decoding/encoding and memory requirements during the conversion and transcoding processes.

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.

Recently, a fast radix-$q$algorithm for an efficient computation of the type-IV discrete cosine transform (DCT-IV) has been proposed in, where$q$is an odd positive integer. In particular, based on the proposed fast algorithm, optimized efficient 3-, 5-, and 9-point scaled DCT-IV (SDCT-IV) modules have been derived in. As a response, an improved efficient optimized 9-point scaled DCT-IV (SDCT-IV) module in terms of the arithmetic complexity is presented. The improved optimized efficient 9-point SDCT-IV module requires 17 multiplications, 53 additions, and three shifts. Consequently, the arithmetic complexity of extended fast mixed-radix DCT-IV algorithm for composite lengths is also significantly improved.

The modified discrete cosine transform (MDCT) is employed in subband/transform coding schemes as the analysis/synthesis filter bank based on time domain aliasing cancellation (TDAC). The most efficient implementation of the forward and inverse MDCT computation for layer III in MPEG-1 and MPEG-2 international audio coding standards is proposed. It is based on a new fast algorithm for the forward and inverse MDCT computation in the oddly stacked system. The complete signal flow graphs for the implementation of MDCT and inverse MDCT in layer III are also provided.

In the above-named aerticle [ibid., vol. 10, pp. -51, Feb. 2001], errors in the expressions of the forward and inverse 9-point DCT/DST modules (p. 51) have been found. Corrected versions of those expressions are presented here.