Online Material: Interactive numerical model of the Mader–Ott Harmonic Analyzer. For contemporary seismological observatory practice and seismic exploration work, the fast Fourier transform (FFT) has become such a common tool that we rarely think about single transforms. Often, we switch from time to frequency to time domain without even examining the spectral data. Restituting seismometer response, calculating source spectra, checking frequency‐dependent attenuation, and doing f − k analysis are only a few applications in seismology, in which the FFT processing steps are an essential tool. Since the advent of modern digital computers, much effort has been made to make the Fourier transform efficient and fast. The basics for the modern transform algorithms were first described by the French mathematician and physicist (Baron) Jean‐Baptiste‐Joseph Fourier (born 21 March 1768 in Auxerre; died 16 May 1830 in Paris). In 1822, he published his seminal work on heat transport in solid‐state bodies, The Analytic Theory of Heat , while at the Ecole Polytechnic Institute in Paris. Fourier not only presented the derivation of the heat transport equations (later called Fourier’s law), but he also proposed a method of resolution, including what we today call a Fourier series. This paper was awarded the prize in mathematics in 1811 by the institute (Herivel, 1975; Bracewell, 1986). Spectral analysis has a long history in the geophysical sciences, with work on the earth’s free oscillations as early as the mid‐nineteenth century (e.g., Lame, 1853). The first recorded seismograph appeared a few decades after Lame’s work and has been credited to Cecchi in 1887 (Dewey and Byerly, 1969). Time series analysis, the analysis of a sequence of signals characterized by a row vector with (usually) real components (Kanasewich, 1981), did not gain wide theoretical treatment until published works by Wiener (1930, 1949) and Kolmogorov (1939) …