## How can I find transfer function from a difference equation?

### Christine Ak (view profile)

on 28 Jun 2013
Latest activity Answered by D. Mike Daniel

### D. Mike Daniel (view profile)

on 10 Oct 2016 at 1:51

### Shashank Prasanna (view profile)

Hey,,I'm new to matlab.

I have homework says that:- y(n)=0.4142y(n-1)+0.2929x(n)+0.2929x(n-1)

find H(z) ?? Plot the poles and zeros on the z-plan with the unit circle ?

Can Somebody help me ,, Please?? thank You !

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### Shashank Prasanna (view profile)

on 28 Jun 2013

This is not a MATLAB question.

Here is some theory:

https://ccrma.stanford.edu/~jos/filters/Z_Transform_Difference_Equations.html

You can certainly plug in those coefficients into tf (in the right way) and it will give you the transfer function.

Christine Ak

### Christine Ak (view profile)

on 28 Jun 2013

Actually My Dr. want it in Matlab :/

I can't find such a way or a function to help me ! Thank You 4 ur help anyway

Shashank Prasanna

### Shashank Prasanna (view profile)

on 28 Jun 2013

Please take a look at the documentation page of TF:

http://www.mathworks.com/help/control/ref/tf.html

You can create the transfer function by passing in the right arguments. I guess that's what the doctor ordered.

Christine Ak

### Christine Ak (view profile)

on 28 Jun 2013

Thank You Soo much I think that helps me...... :)

### D. Mike Daniel (view profile)

on 10 Oct 2016 at 1:51

I'm not sure I fully understand the equation. I also am not sure how to solve for the transfer function given the differential equation. I do know, however, that once you find the transfer function, you can do something like (just for example):

```>> H_z = tf(1, [1 4 6])
```
```H_z =
```
```          1
-------------
s^2 + 4 s + 6```
```Continuous-time transfer function.
```
```>> pzmap(H_z)
```

Where pzmap plots a graph of the poles (marked with "x"s) and zeros (marked with "o"s). This example has no zeros, but has poles at -2 +/- sqrt(2)*i.

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