A fast algorithm for the implementation of filter banks based on `time domain aliasing cancellation´

Several data compression techniques are in competition for coding high-quality audio signals (sampling rate ⩾32 kHz) down to a 64 kb/s bit rate. The authors concentrate on the subband/transform coding scheme using filter banks known as time domain aliasing cancellation (TDAC). This scheme first involves a window on a set of N data, overlapping by N/2 with the previous one, followed by a TDAC transform. First, it is shown that the transform turns out to be a doubly odd DCT, for which a fast algorithm is provided. Then, it is shown how the windowing and the overlap can be merged with the first step of the first algorithm. The total number of operations (multiplications plus additions) required by this algorithm for computing a length-N TDAC plus windowing is exactly N log₂ N. Implementation considerations are provided