Fast odd discrete cosine transform algorithms

It is shown that an N point type I odd discrete cosine transform can be reformulated as a (2N-1) point DFT of a real-symmetric sequence efficiently computed by the real-symmetric PFA-FFT. Using simple index mappings, the type II and III ODCTs are efficiently computed from the ODCT-1 of the same length. The ODCT-IV are then computed from ODCT-II or III using simple recurrence formulas.