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z-Transform

The discrete $z$-transform is defined as

\begin{displaymath}
{\mathcal Z}[a]=\sum_{n=0}^{N-1} a_nz^{kn}.
\end{displaymath} (1)

The Discrete Fourier Transform is a special case of the $z$-transform with
\begin{displaymath}
z\equiv e^{-2\pi i/N}.
\end{displaymath} (2)

A $z$-transform with
\begin{displaymath}
z\equiv e^{-2\pi i\alpha/N}
\end{displaymath} (3)

for $\alpha\not=\pm 1$ is called a Fractional Fourier Transform.

See also Discrete Fourier Transform, Fractional Fourier Transform


References

Arndt, J. ``The $z$-Transform (ZT).'' Ch. 3 in ``Remarks on FFT Algorithms.'' http://www.jjj.de/fxt/.




© 1996-9 Eric W. Weisstein
1999-05-26