### 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}

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 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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Modulo Indexing, Periodic Extension