Convert zero-pole-gain filter parameters to transfer function form

`[b,a] = zp2tf(z,p,k)`

`zp2tf`

forms transfer function polynomials
from the zeros, poles, and gains of a system in factored form.

`[b,a] = zp2tf(z,p,k)`

finds
a rational transfer function

$$\frac{B(s)}{A(s)}=\frac{{b}_{1}{s}^{(n-1)}+\cdots +{b}_{(n-1)}s+{b}_{n}}{{a}_{1}{s}^{(m-1)}+\cdots +{a}_{(m-1)}s+{a}_{m}}$$

given a system in factored transfer function form

$$H(s)=\frac{Z(s)}{P(s)}=k\frac{(s-{z}_{1})(s-{z}_{2})\cdots (s-{z}_{m})}{(s-{p}_{1})(s-{p}_{2})\cdots (s-{p}_{n})}$$

Column vector `p`

specifies the pole locations,
and matrix `z`

specifies the zero locations, with
as many columns as there are outputs. The gains for each numerator
transfer function are in vector `k`

. The zeros and
poles must be real or come in complex conjugate pairs. The polynomial
denominator coefficients are returned in row vector `a`

and
the polynomial numerator coefficients are returned in matrix `b`

,
which has as many rows as there are columns of `z`

.

`Inf`

values can be used as place holders in `z`

if
some columns have fewer zeros than others.

The system is converted to transfer function form using `poly`

with `p`

and
the columns of `z`

.