Power Spectral Density

In the chapter, Power Spectral Density, the problem is the estimation of the PSD of periodic signals buried in noise. The noise signal is of infinite duration and, in practice, observation of the signal is available only over a finite time interval. This constraint makes the estimation of the PSD difficult. There are two basic approaches to do the task. One approach is to use the DFT along with sectionalizing, windowing and averaging. The DFT can also be used after computing the autocorrelation of the data. In this approach, any knowledge of the way the data generated is of no concern. This type is called nonparametric methods. On the other hand, if any knowledge of the way the data generated is available, using that, the approach called parametric methods yields a better estimation of the PSD, in particular, when the data length is relatively short. A linear model to generate the random input data is set up with input as the white noise to the model and the PSD of the model is computed. Another approach is to model the input data as a set of complex exponentials in noise. In this chapter, all the approaches are presented with numerical examples.