Mathematics for Circuits and Filters

4 Fourier Series, Fourier Transforms and the DFT

W. Kenneth Jenkins

University of Illinois, Urbana-Champaign

DOI: 10.1201/9781315214023-4

• 4.1 Introduction
• 4.2 Fourier Series Representation of Continuous Time Periodic SignalsExponential Fourier Series • The Trigonometric Fourier Series • Convergence of the Fourier Series
• 4.3 The Classical Fourier Transform for Continuous Time SignalsProperties of the Continuous Time Fourier Transform • Fourier Spectrum of the Continuous Time Sampling Model • Fourier Transform of Periodic Continuous Time Signals • The Generalized Complex Fourier Transform
• 4.4 The Discrete Time Fourier TransformProperties of the Discrete Time Fourier Transform • Relationship between the Continuous and Discrete ...