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Analysis of Effects on Sound Using the Discrete Fourier Transform

2012, Master of Science, Ohio State University, Mathematics.

The purpose of this study was to show how mathematics can be used to analyze effects on sound. Our hope is that this may inspire student interest in mathematics.


We analyzed five common industry standard effects. Research data was gathered using Mathematica and GarageBand software. Three versions of each effect were used to alter pure tone sound waves of ten different frequencies using GarageBand. Then using Mathematica's Fourier command, the frequency spectrum of each altered sound wave was generated. Through observation of each set of 30 frequency spectra, the most prominent and common pure tone components were determined. For each effect, Mathematica's Fit command was used to determine a best fit model of the magnitude of each component as a function of frequency.


Our models provide descriptions of the effects that are consistent with the traditional descriptions of the industry standard effects in our study. If similar research is to be conducted, our recommendation is that more versions of each effect, a wider range of input frequencies, and a higher sampling rate would produce function models that are even more consistent with traditionally accepted effect descriptions. Furthermore, an understanding of the hardware and software design used to build effects on sound is highly recommended.

Bart Snapp (Advisor)
Herb Clemens (Committee Chair)
James Cogdell (Committee Member)
51 p.

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Tussing, T. (2012). Analysis of Effects on Sound Using the Discrete Fourier Transform. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Tussing, Timothy. "Analysis of Effects on Sound Using the Discrete Fourier Transform." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Tussing, Timothy "Analysis of Effects on Sound Using the Discrete Fourier Transform." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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