The fast Fourier transform for experimentalists. Part I. Concepts

The discrete Fourier transform (DFT) provides a means for transforming data sampled in the time domain to an expression of this data in the frequency domain. The inverse transform reverses the process, converting frequency data into time-domain data. Such transformations can be applied in a wide variety of fields, from geophysics to astronomy, from the analysis of sound signals to CO₂ concentrations in the atmosphere. Over the course of three articles, our goal is to provide a convenient summary that the experimental practitioner will find useful. In the first two parts of this article, we´ll discuss concepts associated with the fast Fourier transform (FFT), an implementation of the DFT. In the third part, we´ll analyze two applications: a bat chirp and atmospheric sea-level pressure differences in the Pacific Ocean.