Introduction to fourier analysis

• Main Authors: Javier, Virginia Regina J., Pinpin, Lovell R.
• Format: text
• Language: English
• Published: Animo Repository 1996
• Subjects: Fourier analysis; Functions, Orthogonal; Fourier transformations; Fourier series
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16307
• Institution: De La Salle University

The primary objective of this paper is to introduce some basic concepts in Fourier analysis. It covers topics such as Fourier series, Fourier transforms, complex Fourier series, generalized functions, and periodic waveforms. These topics are related to each other in the sense that we can associate them with one another. Not only will we present functions that are periodic but we will also focus our attention on nonperiodic functions. Under periodic waveforms are the sine and cosine waveforms which also play a big role in understanding Fourier analysis. Moreover, the sine, cosine, odd, and even functions will have a major part in the study since there are theorems and properties that involve these functions. In fact, these functions are useful tools in studying Fourier series.The paper is expository in nature. Proofs and derivations of formulas and properties in Fourier analysis will be discussed. In addition, trigonometry and calculus will be used to derive solutions for the series.