Image Sampling and Interpolation

In chapter 6, it was demonstrated how signals of finite extent can be mapped into periodic signals. This mapping is mostly of interest because it simplifies the description of signals in terms of a Fourier basis. Operations on periodic signals by linear time- and/or -space-invariant systems (i.e., convolutions) can for instance be described very concisely in the Fourier domain, because the harmonic signals that constitute Fourier bases are eigenvectors of such systems. Hence, periodic signals are adequate mathematical abstractions of signals of finite extent.