Convert transfer function filter parameters to zero-pole-gain form
[z,p,k] = tf2zpk(b,a)
tf2zpk
finds the zeros, poles, and gains
of a discrete-time transfer function.
Note
You should use |
[z,p,k] = tf2zpk(b,a)
finds
the matrix of zeros z
, the vector of poles p
,
and the associated vector of gains k
from the transfer
function parameters b
and a
:
The numerator polynomials are represented as columns
of the matrix b
.
The denominator polynomial is represented in the vector a
.
Given a single-input, multiple output (SIMO) discrete-time system in polynomial transfer function form
$$H(z)=\frac{B(z)}{A(z)}=\frac{{b}_{1}+{b}_{2}{z}^{-1}\cdots +{b}_{n-1}{z}^{-n}+{b}_{n}{z}^{-n-1}}{{a}_{1}+{a}_{2}{z}^{-1}\cdots +{a}_{m-1}{z}^{-m}+{a}_{m}{z}^{-m-1}}$$
you can use the output of tf2zpk
to produce
the single-input, multioutput (SIMO) factored transfer function form
$$H(z)=\frac{Z(z)}{P(z)}=k\frac{(z-{z}_{1})(z-{z}_{2})\cdots (z-{z}_{m})}{(z-{p}_{1})(z-{p}_{2})\cdots (z-{p}_{n})}$$
The following describes the input and output arguments for tf2zpk
:
The vector a
specifies the coefficients
of the denominator polynomial A(z)
in descending powers of z.
The ith row of the matrix b
represents
the coefficients of the i
th numerator polynomial
(the ith row of B(s) or B(z)).
Specify as many rows of b
as there are outputs.
The zero locations are returned in the columns of
the matrix z
, with as many columns as there are
rows in b
.
The pole locations are returned in the column vector p
and
the gains for each numerator transfer function in the vector k
.