Fourier Analysis

Textbook 《投影片下載》

• Ronald N. Bracewell, "The Fourier Transform and Its Applications", 3/e, 2002, McGraw Hill (東華代理)

Reference Books

• H. P. Hsu, "Outline of Fourier Analysis", 1972

• Peter V. O'Neil, "Advanced Engineering Mathematics", 5/e, Thomson Brooks/Cole, 2003 (東華代理)

• Ziemer and Tranter, "Principles of Communications", 5/e, Wiley, 2000 (偉明代理)

Score

• Homework and Programming (30%)

• Midterm Examination (30%)

• Final Examination (40%)

Contents

• 1. Introduction
  1.1 Time domain and Frequency domain
  1.2 Ubiquitous
  1.2 Contents
  1.3 Mathematical Formulas

• 2. Groundwork
  2.1 Infinite series
  2.2 Taylor's series
  2.3 Infinite integral
  2.4 Algebra and Linear Algebra
  2.5 Signal Space expansion
  2.6 Convolution
  2.7 Serial products
  2.8 Convolution of discrete-time signal
  2.9 Properties of convolution
  2.10 Delta function

• 3. Fourier Serie
  3.1 Fourier series (for periodic function)
  3.2 Approximation by Finite Fourier series
  3.3 Convergence of Fourier series (Dirichlet condition)
  3.4 Differentiation and Integration of Fourier series
  3.5 Fourier series of symmetric functions
  3.6 Fourier expansion a function over a finite interval
  3.7 Fourier series of derivation of discontinuous periodic function
  3.8 Discrete frequency spectra
  3.9 Parseval's Theorem

• 4. Continuous-Time Fourier Transform
  4.1 From Fourier Series to Fourier Transform
  4.2 Fourier Transform
  4.3 Conditions for the Existence of Fourier Transform
  4.4 Important Examples
  4.5 Properties
  4.6 Symmetric property of Fourier Transform
  4.7The Fourier transform of a periodic function
  4.8 The Fourier transform of generalized function

• 5. Discrete-Time Fourier Series and Transform
  5.1 Representation of periodic sequences: the discrete Fourier series (DFS)
  5.2 Properties of the discrete Fourier series
  5.3 The Discrete-Time Fourier transform
  5.4 Symmetric property of discrete-time Fourier Transform (DT-FT)
  5.5 Conditions for the Existence of Fourier Transform

• 6. Discrete Fourier Transform (DFT) and FFT
  6.1 Sampling the Fourier transform
  6.2 Fourier representation of finite-duration sequences: the discrete Fourier transform (DFT)
  6.3 Properties of the discrete Fourier transform
  6.4 Linear convolution using the discrete Fourier transform
  6.5 Efficient computation of the discrete Fourier transform
  6.6 Goertzel algorithm
  6.7 Decimation-in-time FFT algorithms
  6.8 Decimation-in-frequency FFT algorithms
  6.9 The discrete cosine transform (DCT)

• 7. Application to Communication Theory
  7.1 Sampling theory
  7.2 Correlation function
  7.3 Power spectral density and correlation