### Operator Notation

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 :

*e.g.*,

*parameters*affecting their definition. For example the

*shift operator*(defined in §7.2.3 below) requires a

*shift amount*:

^{7.3}

*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 signal-processing 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.(7.8)), and it is much closer to how things look in a readable computer program (such as in the matlab language).

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Flip Operator

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