TABLE OF CONTENTS In this book, we will describe a special instance of digital signal processing. A signal is simply a function of time, space, or both (here we will stick to time for brevity). Time can be viewed as either continuous or discrete; equally, the amplitude of the function (signal) can be either continuous or discrete. Although we are actually interested in discrete-time, discrete-amplitude signals, ideas from the continuous-time, continuous amplitude domain have played a vital role in digital signal processing, and we cross this frontier freely in our exposition.
A digital signal, then, is a sequence of real or complex numbers, i.e., a vector in a finite-dimensional vector space. For real-valued signals, this is modelled on R n, and for complex signals, C n. Vector addition corresponds to superposition of signals, while scalar multiplication is amplitude scaling (including sign reversal). Thus, the concepts of vector spaces and linear algebra are natural in signal processing. This is even more so in digital image processing, since a digital image is a matrix. Matrix operations in fact play a key role in digital image processing. We now quickly review some basic mathematical concepts needed in our exposition; these are more fully covered in the literature in many places, for example in [8], [9] and [7], so we mainly want to...
