In this book, an operator is defined as a signal-valued function of a signal. Thus, for the space of length complex sequences, an operator is a mapping from to :
Note that operator notation is not standard in the field of digital signal processing. It can be regarded as being influenced by the field of computer science. In the Fourier theorems below, both operator and conventional mathematical notations are provided. In the author's opinion, operator notation is consistently clearer, allowing powerful expressions to be written naturally in one line (e.g., see Eq. (7.10)), and it is much closer to how things look in a maximally readable computer program (such as in the matlab language).