Zero-pole plot

`zplane(z,p)`

zplane(b,a)

zplane(d)

[hz,hp,ht] = zplane(z,p)

This function displays the poles and zeros of discrete-time systems.

`zplane(z,p)`

plots the zeros
specified in column vector `z`

and the poles specified
in column vector `p`

in the current figure window.
The symbol `'o'`

represents a zero and the symbol `'x'`

represents
a pole. The plot includes the unit circle for reference. If `z`

and `p`

are
arrays, `zplane`

plots the poles and zeros in the
columns of `z`

and `p`

in different
colors.

`zplane(b,a)`

where `b`

and `a`

are
row vectors, first uses `roots`

to
find the zeros and poles of the transfer function represented by numerator
coefficients `b`

and denominator coefficients `a`

.
The transfer function is defined in terms of *z*^{–1}:

$$H(z)=\frac{B(z)}{A(z)}=\frac{b(1)+b(2){z}^{-1}+\cdots +b(n+1){z}^{-n}}{a(1)+a(2){z}^{-1}+\cdots +a(m+1){z}^{-m}}$$

`zplane(d)`

finds the zeros
and poles of the transfer function represented by the digital filter, `d`

.
Use `designfilt`

to generate `d`

based
on frequency-response specifications. The pole-zero plot is displayed
in `fvtool`

.

`[hz,hp,ht] = zplane(z,p)`

returns
vectors of handles to the zero lines, `hz`

, and the
pole lines, `hp`

. `ht`

is a vector
of handles to the axes/unit circle line and to text objects, which
are present when there are multiple zeros or poles. If there are no
zeros or no poles, `hz`

or `hp`

is
the empty matrix `[]`

.

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