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Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals

The combination of the time-discrete property of digital signals together with the commonly employed definition of the discrete Fourier transform (DFT) can cause ambiguity when interpreting magnitude spectra with respect to the physical unit of the signal under consideration. Standardized scaling of spectra increases the comparability of frequency-domain data that are published in scientific articles or data sheets of commercial products. We present and discuss in this tutorial a collection of the most relevant scaling options for DFT spectra to yield amplitude spectra, power spectra, and power density spectra, and we illustrate how an implied physical unit of the underlying signal is reflected by the magnitude of the spectrum. The tutorial is accompanied by Matlab/Octave scripts that demonstrate the different cases.

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