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# evalfr

Evaluate frequency response at given frequency

## Syntax

frsp = evalfr(sys,f)

## Description

frsp = evalfr(sys,f) evaluates the transfer function of the TF, SS, or ZPK model sys at the complex number f. For state-space models with data (ABCD), the result is

H(f) = D + C (fI – A)–1B

evalfr is a simplified version of freqresp meant for quick evaluation of the response at a single point. Use freqresp to compute the frequency response over a set of frequencies.

## Examples

### Example 1

To evaluate the discrete-time transfer function

$H\left(z\right)=\frac{z-1}{{z}^{2}+z+1}$

at z = 1 + j, type

```H = tf([1 -1],[1 1 1],-1);
z = 1+j;
evalfr(H,z)
```

to get the result:

```ans =
2.3077e-01 +  1.5385e-01i
```

### Example 2

To evaluate the frequency response of a continuous-time IDTF model at frequency w = 0.1 rad/s, type:

```sys = idtf(1,[1 2 1]);
w = 0.1;
s = 1j*w;
evalfr(sys, s)```

The result is same as freqresp(sys, w).

## Limitations

The response is not finite when f is a pole of sys.