Finite Fourier

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

doi:10.1007/978-3-030-00982-3_8

Finite Fourier

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

Music (Twin Cities)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

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 language	English (US)
Title of host publication	Computational Music Science
Publisher	Springer Nature
Pages	75-91
Number of pages	17
DOIs	https://doi.org/10.1007/978-3-030-00982-3_8
State	Published - 2018

Publication series

Name	Computational Music Science
ISSN (Print)	1868-0305
ISSN (Electronic)	1868-0313

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© 2018, Springer Nature Switzerland AG.

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AU - Mazzola, Guerino

AU - Pang, Yan

AU - Heinze, William

AU - Gkoudina, Kyriaki

AU - Pujakusuma, Gian Afrisando

AU - Grunklee, Jacob

AU - Chen, Zilu

AU - Hu, Tianxue

AU - Ma, Yiqing

PY - 2018

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Finite Fourier

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