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Published in:
2019 | OriginalPaper | Chapter
1. Fourier Transform
Author : Dr. Dengsheng Zhang
Published in: Fundamentals of Image Data Mining
Publisher: Springer International Publishing
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Abstract
This chapter presents an evolutional journey from Fourier series to Fourier transform and to discrete Fourier transform. It aims to prepare readers with mathematical fundamentals and build a foundation for understanding wavelet theories. It begins with sinusoids that are the building blocks of Fourier transform. After the fundamental properties of sinusoids are understood, Fourier series and Fourier transform are formally introduced. It is followed by describing DFT and sampling theory. The connection between DFT and its application on signal processing is systematically revealed to the readers. By finishing the Fourier transform chapter, readers will be able to understand the power and limitations of Fourier transform, this naturally leads to windowed FT in the following chapter.