On computing DFT of real N-point vector and IDFT of DFT-transformed real N-point vector via single DFT

This article presents a method to compute the discrete Fourier transform (DFT) of an N-point real vector and the inverse DFT (IDFT) of the DFT of another real N-point vector by carrying out a single complex N-point DFT. Possible applications are for transceivers where the transmitter has to carry out the DFT of an N-point real sequence and the receiver has to carry out the inverse DFT of the DFT of another N-point real sequence.