Efficient input reordering for the DCT based on a real-valued decimation-in-time FFT

The possibility of computing the discrete cosine transform (DCT) of length N=2/sup v/, v integer, via an N-point discrete Fourier transform (DFT) is widely known from the literature. It is demonstrated that this computation can be done in place by just employing butterfly swaps if the input reordering (necessary for the DCT computation via DFT) is combined with the bit-reverse scrambling required by the real-valued version of the decimation-in-time fast Fourier transform algorithm. As computer code for many real-valued FFT algorithms is publicly available, and FFT-based DCT computations exhibit a very regular structure that is helpful in signal processor implementations, this method of DCT-computation becomes even more attractive.