Introduction to Frequency Analysis: The Fourier Transformation
The Fourier transformation is a key mathematical tool that connects the time and frequency domains such that sound can be parametrized in terms of frequency. The theory of the different Fourier transforms, including the inverse transform, is presented to facilitate the reading of the following chapters. Each mathematical equation is translated into R so that the basic principles can be understood and unmystified. This discovery of the Fourier transformation is accompanied with the presentation of the frequency spectrum, the phase spectrum, the different frequency scales, the Fourier window shapes, and the cepstrum.
- Bogert BP, Healy MJR, Tukey JW (1963) The quefrency alanysis of time series for echoes: cepstrum, pseudo-autocovariance, cross-cepstrum, and saphe cracking. In: Time series analysis. Wiley, New York, pp 209–243Google Scholar
- Hartmann WM (1998) Signals, sound, and sensation. Springer, New YorkGoogle Scholar