Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals
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J. Ahrens, C. Andersson, P. Höstmad, and W. Kropp, "Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals," Engineering Brief 600, (2020 May.). doi:
J. Ahrens, C. Andersson, P. Höstmad, and W. Kropp, "Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals," Engineering Brief 600, (2020 May.). doi:
Abstract: 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.
@article{ahrens2020tutorial,
author={ahrens, jens and andersson, carl and höstmad, patrik and kropp, wolfgang},
journal={journal of the audio engineering society},
title={tutorial on scaling of the discrete fourier transform and the implied physical units of the spectra of time-discrete signals},
year={2020},
volume={},
number={},
pages={},
doi={},
month={may},}
@article{ahrens2020tutorial,
author={ahrens, jens and andersson, carl and höstmad, patrik and kropp, wolfgang},
journal={journal of the audio engineering society},
title={tutorial on scaling of the discrete fourier transform and the implied physical units of the spectra of time-discrete signals},
year={2020},
volume={},
number={},
pages={},
doi={},
month={may},
abstract={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.},}
TY - paper
TI - Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals
SP -
EP -
AU - Ahrens, Jens
AU - Andersson, Carl
AU - Höstmad, Patrik
AU - Kropp, Wolfgang
PY - 2020
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - May 2020
TY - paper
TI - Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals
SP -
EP -
AU - Ahrens, Jens
AU - Andersson, Carl
AU - Höstmad, Patrik
AU - Kropp, Wolfgang
PY - 2020
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - May 2020
AB - 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.
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.
Authors:
Ahrens, Jens; Andersson, Carl; Höstmad, Patrik; Kropp, Wolfgang
Affiliation:
Chalmers University of Technology
AES Convention:
148 (May 2020)eBrief:600
Publication Date:
May 28, 2020Import into BibTeX
Subject:
Signal Processing
Permalink:
http://www.aes.org/e-lib/browse.cfm?elib=20838
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