On the odd-DFT and its applications to DCT/IDCT computation

In this correspondence, efficient algorithms are presented for simultaneous calculation of the odd discrete Fourier transform (odd-DFT) and the real DFT. These algorithms are used to derive a new algorithm to calculate the discrete cosine transform (DCT) that is computationally equivalent to the classical fast Fourier transform (FFT)-based algorithm for DCT calculation . In addition, odd-DFT properties are exploited to develop a novel algorithm for an inverse discrete cosine transform (IDCT) calculation that outperforms previous FFT-based solutions for IDCT calculation