# ctranspose, '

Conjugate dynamic system model

## Syntax

``H = ctranspose(G)``

## Description

example

````H = ctranspose(G)` computes the conjugate of the dynamic system model or static model `G`. The `ctranpose` command is equivalent to the `'` operator. If `G` is a dynamic system model poles P and zeros Z, then the conjugate system `H = ctranspose(G)= G'` has the following properties.In continuous time, the poles of `H` are –P and the zeros of `H` are –Z. The frequency response of H is the Hermitian transpose of the frequency response of G:H(jω) = G(jω)H.In discrete time with sample time Ts, the poles of `H` are 1/P and the zeros of `H` are 1/Z. The frequency response of H is the Hermitian transpose of the frequency response of G:H(z) = G(z)H,where z = eiωTs.If `G` is a static model, then `H` is the complex-conjugate transpose of the matrix.```

## Examples

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Compute the conjugate of a one-input, two-output transfer function model.

```s = tf('s'); G1 = (s + 1)/(s^2 + 2*s + 1); G2 = 1/s; G = [G1;G2]```
```G = From input to output... s + 1 1: ------------- s^2 + 2 s + 1 1 2: - s Continuous-time transfer function. ```

The conjugate has two outputs and one input, and takes s to –s.

`H = ctranspose(G)`
```H = From input 1 to output: -s + 1 ------------- s^2 - 2 s + 1 From input 2 to output: -1 -- s Continuous-time transfer function. ```

Using the `'` operator yields the same result as `ctranspose`.

`H = G'`
```H = From input 1 to output: -s + 1 ------------- s^2 - 2 s + 1 From input 2 to output: -1 -- s Continuous-time transfer function. ```

Obtain the frequency response and the Hermitian transpose of the frequency response of a transfer function at one frequency.

```G = [tf(1,[1 0]);tf([1 0],[1 1])]; w = 3; resp = freqresp(G,w)```
```resp = 2×1 complex 0.0000 - 0.3333i 0.9000 + 0.3000i ```

The Hermitian transpose of the frequency response is the frequency response of the conjugate of `G`.

`respH = freqresp(G',w)`
```respH = 1×2 complex 0.0000 + 0.3333i 0.9000 - 0.3000i ```

## Input Arguments

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Input system, specified as a dynamic system model or static model such as a `tf`, `zpk`, or `ss` model. `G` can be a generalized model provided that its control design blocks are scalar and nondynamic, such as a scalar `ureal` parameter.

## Output Arguments

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Conjugate model of `G`, returned as a dynamic system model or static model of the same type as `G`.

## Version History

Introduced before R2006a