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

Note 27. Exploring Periodogram Performance: Sinusoids in Additive White Gaussian Noise

This note demonstrates how the unmodified periodogram’s ability to resolve sinusoidal components with distinct frequencies varies with both the signal-to-noise ratio and the frequency separation of the components. In subsequent notes, similar techniques are used to assess the performance of other types of periodograms—most of which outperform the unmodified periodogram.

27.1. SNR Variations

The MATLAB code in Computer Listing 27.1 generates two cosine waves embedded in additive white Gaussian noise (AWGN) and then computes the unmodified periodogram for the composite signal. This code was run for the combinations of frequency and SNR listed in Table 27.1 ...