The
chirp Z-transform (CZT), useful in evaluating the Z-transform along
contours other than the unit circle. The chirp Z-transform is also
more efficient than the DFT algorithm for the computation of prime-length
transforms, and it is useful in computing a subset of the DFT for
a sequence. The chirp Z-transform, or CZT, computes the Z-transform
along spiral contours in the *z*-plane for an input
sequence. Unlike the DFT, the CZT is not constrained to operate along
the unit circle, but can evaluate the Z-transform along contours described
by *z _{ℓ}* =

One possible spiral is

A = 0.8*exp(j*pi/6); W = 0.995*exp(-j*pi*.05); M = 91; z = A*(W.^(-(0:M-1))); zplane([],z.')

`czt(x,M,W,A)`

computes the Z-transform of `x`

on
these points.

An interesting and useful spiral set is `m`

evenly
spaced samples around the unit circle, parameterized by `A = 1`

and `W = exp(-j*pi/M)`

. The Z-transform on this contour
is simply the DFT, obtained by

y = czt(x)

Was this topic helpful?