Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 26. Unmodified Periodogram

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, S_U [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):

26.1

where X [m] is the slightly modified DFT given by

26.2 ...