This note presents the definition and basic properties of the unmodified periodogram. The unmodified periodogram is the simplest of the classical, nonparametric, DFT-based methods that are used to estimate the power spectrum of a discrete-time signal. Examples of its performance against various signal combinations and noise conditions are also presented.
For a discrete-time signal, x[n], the unmodified periodogram, SU [m], is computed as the normalized, squared magnitude of the N-point DFT for an L-sample segment of the signal that has been padded with N – L zeros (see Note 16: Exploring DFT Resolution for a discussion of zero-padding in the DFT):
where X [m] is the slightly modified DFT given by