The bilateral z transform of the discrete-time signal
is
defined to be
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(7.2) |
Recall (§4.1) that the mathematical representation of a
discrete-time signal
maps each integer
to a complex
number (
) or real number (
). The z transform
of
, on the other hand,
, maps every complex number
to a new complex number
. On a higher
level, the z transform, viewed as a linear operator, maps an entire
signal
to its z transform
. We think of this as a ``function to
function'' mapping. We may say
is the z transform of
by writing
or, using operator notation,
which can be abbreviated as
One also sees the convenient but possibly misleading notation
The z transform of a signal
can be regarded as a polynomial in
, with coefficients given by the signal samples. For example,
the signal
has the z transform