Finite Fourier

Guerino Mazzola, Yan Pang, William Heinze, Kyriaki Gkoudina, Gian Afrisando Pujakusuma, Jacob Grunklee, Zilu Chen, Tianxue Hu, Yiqing Ma

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationComputational Music Science
PublisherSpringer Nature
Number of pages17
StatePublished - 2018

Publication series

NameComputational Music Science
ISSN (Print)1868-0305
ISSN (Electronic)1868-0313

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature Switzerland AG.


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