C. Sequence of Systems -- D. Mapping of Deconvolution to Division -- II. Shift/Modulation -- A. Modulation of a Carrier -- III. Change in Scale -- IV. Mapping of Differential Equations to Polynomial Equations -- V. Fourier Transform of Even and Odd Signals -- A. Quadrature Signals -- VI. The Sine Function -- VII. Value at the Origin and the Integral in the Other Domain -- VIII. Conservation of Energy -- IX. Uncertainty Principle -- X. Heuristics -- XI. Summary -- XII. Further Reading -- References -- Chapter 17 -- Polynomial Transform -- I. Signals of Limited Complexity -- II. Polynomial Representation of a Signal -- III. Sample Representation of a Signal -- IV. Evaluation -- V. Interpolation -- VI. Polynomial Multiplication -- VII. Mapping of a Convolution to Multiplication -- VIII. Summary -- IX. Further Reading -- References -- Chapter 18 -- Discrete Fourier Transform -- I. Continuous Discrete Digital -- II. Periodic Signals -- A. Representation of a Limited Extent Signal by a Periodic Signal -- B. Shifting -- III. Discrete Fourier Transform -- A. Examples of Discrete Fourier Transform Pairs -- B. Basis Functions -- C. Periodicity of the Discrete Fourier Transform -- D. Definition of the Discrete Fourier Transform on any N Point Interval -- IV. Sum of Basis Functions -- V. Proof of the Discrete Fourier Transform Relation -- VI. Analogy between Vectors and the Discrete Signals -- VII. Fast Fourier Transform -- VIII. Summary -- IX. Further Reading -- References -- Chapter 19 -- Vector Space Rotation -- I. Example of a Rotation Operation -- II. Rotation of a Vector Space -- III. The Discrete Fourier Transform as a Rotation -- IV. Matrix Rotation -- V. Rotation to an Eigenvectors Basis -- VI. Example of the Rotation of a System to an Eigenvector Basis -- VII. Analogy between Matrix Rotations and Linear Systems -- VIII. Summary -- IX. Further Reading