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Finite Fourier

  • Guerino Mazzola
  • Yan Pang
  • William Heinze
  • Kyriaki Gkoudina
  • Gian Afrisando Pujakusuma
  • Jacob Grunklee
  • Zilu Chen
  • Tianxue Hu
  • Yiqing Ma
Chapter
Part of the Computational Music Science book series (CMS)

Summary.

Following the brief introduction to Fourier theory in Chapter 4.1, we will now discuss finite Fourier analysis, which confines the periodic Fourier formula to a finite number of overtones. We further introduce Nyquist’s Sampling Theorem, which connects the highest overtone frequency with the sample rate. This chapter also introduces the Fast Fourier Transform (FFT), which increases the calculation efficiency of Fourier’s formula by using complex numbers. Later in this chapter we talk about compression technologies, audio formats in various resolutions, and how they differ.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Guerino Mazzola
    • 1
  • Yan Pang
    • 1
  • William Heinze
    • 1
  • Kyriaki Gkoudina
    • 1
  • Gian Afrisando Pujakusuma
    • 1
  • Jacob Grunklee
    • 1
  • Zilu Chen
    • 1
  • Tianxue Hu
    • 1
  • Yiqing Ma
    • 1
  1. 1.School of MusicUniversity of MinnesotaMinneapolisUSA

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