The fast Fourier transform for experimentalists

In part one of this series, we discussed several basic properties of the fast Fourier transform (FFT). In addition to fundamental elements, we treated zero padding, aliasing, the relationship to a Fourier series, and ended with an introduction to windowing. In part II, we continue our discussion with a more general approach to spectrum estimation, including the periodogram, the autocorrelation function, autoregressive spectral estimation, and maximum entropy spectral estimation. In addition, we include brief descriptions of treating convolution, filtering, and detrending. In the final installment, as we treat several applications, we draw on a number of the ideas discussed in the first part dealing with concepts and then apply some of the methods. The particular applications we consider include the spectral analysis of a bat chirp, atmospheric sea-level pressure differences, and perhaps even take a look, at atmospheric CO₂.