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DISCRETE AND CONTINUOUS FOURIER TRANSFORMS
ANALYSIS, APPLICATIONS AND FAST ALGORITHMS

DISCRETE AND CONTINUOUS FOURIER TRANSFORMS
ANALYSIS, APPLICATIONS AND FAST ALGORITHMS

University of Guelph Guelph, Ontario, Canada

Eleanor Chu

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List of Figures List of Tables Preface Acknowledgments About the Author xi xv xvii xxi xxiii

I Fundamentals, Analysis and Applications
1 Analytical and Graphical Representation of Function Contents 1.1 Time and Frequency Contents of a Function . . . . . . . . 1.2 The Frequency-Domain Plots as Graphical Tools . . . . . 1.3 Identifying the Cosine and Sine Modes . . . . . . . . . . . 1.4 UsingComplex Exponential Modes . . . . . . . . . . . . 1.5 Using Cosine Modes with Phase or Time Shifts . . . . . . 1.6 Periodicity and Commensurate Frequencies . . . . . . . . 1.7 Review of Results and Techniques . . . . . . . . . . . . . 1.7.1 Practicing the techniques . . . . . . . . . . . . . . 1.8 Expressing Single Component Signals . . . . . . . . . . . 1.9 General Form of a Sinusoid in SignalApplication . . . . . 1.9.1 Expressing sequences of discrete-time samples . . 1.9.2 Periodicity of sinusoidal sequences . . . . . . . . 1.10 Fourier Series: A Topic to Come . . . . . . . . . . . . . . 1.11 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....