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# Digital first-order IIR filter impulse response

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#### Sandi2000

##### Junior Member level 2
The first formula :
A causal first-order IIR filter is characterized by the following difference equation

(01)

The impulse response of that system can be computed via the Z-transform or otherwise, and it turns out to be
(02)

The second formula :
the general causal IIR filter is

(03)

has transfer function
(04)

one step of long division yields

(05)

The question is :

The common thing between the first and second formula is (b1−b0*a1) ,i want to understand more why using (b1−b0*a1) in first and second formula? what is the difference ?

The question is :
The common thing between the first and second formula is (b1−b0*a1) ,
i want to understand more why using (b1−b0*a1) in first and second formula?
what is the difference ?
Nb >= Na.

Sandi2000

### Sandi2000

Points: 2
Nb >= Na.

Yes i agree with you , the problem is ,when can I apply the equation (2) and when can i apply the equation (5)?

when can I apply the equation (2)
and when can i apply the equation (5)?
Describe sentences gramatically correctly.

Numbers of Pole are different for (2) and (5).
Can you understand ?

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Sandi2000

Points: 2