# FIR-IIR ?

FIR : Finite Impulse Response IIR : Infinite Impulse Response |

We could fill multiple pages to explain in detail what this really means in detail and dig deep into the theory of those two types of filters and their respective advantages and disadvantages. That’s not the goal of this article. You will find multiple documents all over the internet offering much more detailed information on the subject.

For our purposes we will very much simplify and state the following:

FIR filters are linear phase filters. This means that for all frequencies, the induced delay by the filter will be the same. This delay is known as group delay and is constant.

IIR filters are minimal phase filters. The group delay for each frequency is different, thus the group delay is not constant.

Let’s have a look at a practical application.

- Direct comparison between the same value filters in FIR and IIR
- IIR Linkwitz-Riley 24db/oct low pass filter at 150 Hz:

- IIR Linkwitz-Riley 24db/oct high pass filter at 150 Hz:

- IIR low pass and high pass summing :

- FIR Linkwitz-Riley 24db/oct low pass filter at 150 Hz:

- FIR Linkwitz-Riley 24db/oct high pass filter at 150 Hz:

- FIR low pass and high pass summing:

- Direct comparison between IIR and FIR equalization:

- Other characteristics

On this last plot we see that’s the summing of the low pass and high pass gives a flat frequency response. Phase response is a 360° rotation (180 degrees from 20Hz to 150Hz which is the cut-off frequency and another 180 degrees phase shift from 150Hz to 20 KHz). That means all frequencies through the filter will not have the same group delay. **Low frequencies are delayed with respect to higher frequencies.**

Let’s have a look at the same situation using FIR filters:

On this last plot we see that’s the summing of the low pass and high pass gives a flat frequency response as do IIR filters but in comparison and most important the phase response remains linear.

That means all frequencies going through the filter will have the same group delay. **Low frequencies are NOT delayed with respect to higher frequencies.**

**Blue curve:** FIR amplitude response

**Red curve:** IIR amplitude response

**Dashed red and blue curves:** IIR and FIR amplitude response

The amplitude response for both filters is pretty similar, they differ noticeably in phase response though. The IIR phase response is altered.

The main advantage of FIR as shown above is that the frequency response can be changed without altering phase response.

Both amplitude and phase response are independent from each other.

This also means that you can modify phase response without altering the amplitude response.

The examples hereunder show the use of a parametric phase equalizer.

The frequency response remains unaltered.

This characteristic of FIR filters is the most interesting as it allows the user to directly correct one of the main problems with sound reproduction in the automotive passenger’s compartment.

The FIR filters can be freely attributed in our new DSP NX signal processor and allow you to reestablish the acoustic phase of the loudspeakers.