Efficient computation of DFT of Zadoff-Chu sequences

An important property of a Zadoff-Chu (ZC) sequence is derived, namely that the discrete Fourier transform (DFT) of a ZC sequence is a time-scaled conjugate of the ZC sequence, multiplied by a constant factor. This result has many practical applications. For example, it can be used to generate 3GPP LTE access preambles more efficiently than the standard suggests as it allows the DFT of a ZC sequence of prime length P to be computed with P instead of PlogP arithmetic operations.