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# zp2tf

Zero pole gain to transfer function

### Syntax

```S = zp2tf(z, p, k)
S = zp2tf(z, p, k, dt)```

### Arguments

z

a real or complex matrix, the ith column contains the transmission zeros relative to the ith output. If some zeros are complex, they must appear in complex conjugate pairs.

If the number of zeros relative to the ith output is less than the max number of zeros for each output, the ith column must be padded with %inf values.

p

a real or complex vector, the poles of the system. If some poles are complex, they must appear in complex conjugate pairs.

If the number of poles relative to the ith output is less than the max number of poles for each output, the ith column must be padded with %inf values.

k

a real scalar or a real vector, the ith element contains the gain relative to the ith output.

dom

a character string with possible values "c" or "d", [] or a real positive scalar, the system time domain (see syslin).

S

a single input transfer function.

### Description

Converts a zero pole gain representation to rational transfer function

### Examples

```Z=[2;1];P=[0;-3-%i;-3+%i];K=2.5;
S=zp2tf(Z,P,K,"c")
roots(S.num)```

### See Also

• zp2ss — Zero pole gain to state space

### History

 Version Description 6.0 Function added.
 Report an issue << zp2ss Linear System Representation zpk >>

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