Chapter 1

Two-Dimensional Signals and Systems

This chapter sets forth the main concepts of two-dimensional (2-D) signals and systems as extensions of the linear systems concepts of 1-D signals and systems. We concentrate on the discrete-space case of digital data, including the corresponding 2-D Fourier transform. We also introduce the continuous-space Fourier transform to deal with angular rotations and prove the celebrated projection-slice theorem of computer tomography. In later chapters we will encounter the central role of motion compensation in image sequences and video, where motion is often not an exact number of pixels, which makes the interplay of discrete parameters and continuous parameters quite important. While this first chapter ...

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