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tf2zp() - Signal Processing

```tf2zp finds the zeros, poles, and gains of
a continuous-time transfer function. Note

You should use tf2zp when working with positive
powers (s2 + s + 1), such as in continuous-time transfer
functions. A similar function, tf2zpk,
is more useful when working with transfer functions expressed in inverse
powers (1 + z-1 + z-2), which
is how transfer functions are usually expressed in DSP.[z,p,k] = tf2zp(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 SIMO continuous-time system in polynomial transfer function
formH(s)=B(s)A(s)=b1sn−1+⋯+bn−1s+bna1sm−1+⋯+am−1s+amyou can use the output of tf2zp to produce
the single-input, multi-output (SIMO) factored transfer function formH(s)=Z(s)P(s)=k(s−z1)(s−z2)⋯(s−zm)(s−p1)(s−p2)⋯(s−pn)The following describes the input and output arguments for tf2zp:The vector a specifies the coefficients
of the denominator polynomial A(s)
(or A(z)) in
descending powers of s (z-1). The ith row of the matrix b represents
the coefficients of the ith numerator polynomial
(the ith row of B(s)
or B(z)). Specify as many rows
of b as there are outputs. For continuous-time systems, choose the number nb of
columns of b to be less than or equal to the length na of
the vector a.For discrete-time systems, choose the number nb of
columns of b to be equal to the length na of
the vector a. You can use the function eqtflength to provide equal length vectors
in the case that b and a are
vectors of unequal lengths. Otherwise, pad the numerators in the matrix b (and,
possibly, the denominator vector a) with zeros.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. The tf2zp function is part of the standard MATLAB® language.```

Syntax

`[z,p,k] = tf2zp(b,a)`

Example

```Zeros, Poles, and Gain of a Continuous-Time SystemOpen This Example
Generate a system with the following transfer function.

Find the zeros, poles, and gain of the system. Use eqtflength to ensure the numerator and denominator have the same length. Plot the poles and zeros to verify that they are in the expected locations.
b = [2 3];
a = [1 1/sqrt(2) 1/4];
fvtool(b,a,'polezero')
[b,a] = eqtflength(b,a);
[z,p,k] = tf2zp(b,a)
text(real(z)+.1,imag(z),'Zero')
text(real(p)+.1,imag(p),'Pole')

z =

0
-1.5000

p =

-0.3536 + 0.3536i
-0.3536 - 0.3536i

k =

2```