Implementation Of MDCT Based On First-order Moments

The modified discrete cosine transform (MDCT) is an efficient time-frequencyanalysis tool, and it has been widely used in audio coding. MDCT also has very importanttheory and broad application value. In this paper, according to the thought of the fastfirst-order moment computation algorithm without multiplier proposed by Professor.Liu,we decide to use first-order moment to improve the computation of MDCT. First weestablish a new computing formula for MDCT by transforming this input sequence into afirst-order moment using given principle, which results in that the computation of theMDCT could be implemented by the first-order moment. Then by introducing two fastmoment structures to compute the first-order moment, the proposed algorithms couldimplement the MDCT without multiplications and limitations on the length of MDCT, andtheir computational structures are simpler compared with the traditional algorithms of theMDCT. Furthermore, since not only the MDCT but the introduced algorithms of momentscould also be performed by the systolic array, we design new systolic array for MDCTbased on our approach. A very simple and scalable systolic array without multipliers andROMs has also been designed to perform the arbitrary length MDCT, which can make theVLSI implementation more efficient and easier. Finally the comparison with three existingmethods shows the superiority of our method.