Discussion : FIR vs IIR filters: Add your comments

Started by utd_anurag September 3, 2004
Hi,
I am new to this group.
I want to initiate a discussion pertaining to FIR and IIR filters.
I am adding my beliefs & have a few questions.

Please do add your comments and suggestions.. if any.. Thanks,

FIR filters:

1). depend on previous i/p samples.
2). have linear phase-charateristics.
3). used in applications where we need a linear phase-characteristic.
4). delay characteristics are better than IIR filters.
5). require more memory.

IIR filters:

1). depend on the previous i/p as well as o/p samples.
2). don' t have linear phase-charateristics.
3). used in applications where linearity is not a big-issue.
4). consists of zeros as well as poles.
5). require less memory but complex to implement.
6). when there is delay-adjustment & distortion-adjustment, the
location of poles & zeros can vary and may lie outside the unit
circle; thus making the filter unstable.
7). IIR filter works well..for lower-order tappings. Might be
unstable for higher-order tappings.

Please correct wrong points.

I have the following questions:

1). Is FIR an all-zero/all-pole/mixed filter?
2). If IIR filter is having such instability issues..then why do we
use IIR filters.??
3). In which applications.. do we use an IIR filter???
4). Which is a better equalizer...FIR or IIR?
5). Is there any condition..when an IIR filter can act as a LINEAR
FILTER?



--- In , "utd_anurag" <utd_anurag@y...> wrote:
> Hi,
> I am new to this group.
> I want to initiate a discussion pertaining to FIR and IIR filters.
> I am adding my beliefs & have a few questions.
>
> Please do add your comments and suggestions.. if any.. > Thanks,
>
> FIR filters:
>
> 1). depend on previous i/p samples.
> 2). have linear phase-charateristics.
> 3). used in applications where we need a linear phase-
characteristic.
> 4). delay characteristics are better than IIR filters.
> 5). require more memory.
FIR filters also are always stable
> IIR filters:
>
> 1). depend on the previous i/p as well as o/p samples.
> 2). don' t have linear phase-charateristics.
You can actually design IIR filters that will exhibit linear phase
characteristics, but you must design accordingly, please see MITRA
for reference on this topic (very good matlab / DSP book )
> 3). used in applications where linearity is not a big-issue.
not necessarly, see above
> 4). consists of zeros as well as poles.
yes, so beaware of stability issues
> 5). require less memory but complex to implement.
I wouldn't say they are complex to implement, they are really
straight forward to implement in hardware (DSPs or FPGA). They are
much faster ( on average) than FIR filters.
> 6). when there is delay-adjustment & distortion-adjustment, the
> location of poles & zeros can vary and may lie outside the unit
> circle; thus making the filter unstable.
yup, must becareful and know your application.
> 7). IIR filter works well..for lower-order tappings. Might be
> unstable for higher-order tappings.
again, this is more of a design statement, than a general fact.
Basic IIR implementations this is probably true, but don't believe
that is always the case, check out MITRA on this topic as well.
>
> Please correct wrong points.
>
> I have the following questions:
>
> 1). Is FIR an all-zero/all-pole/mixed filter?
FIRs have a transfer function of the order H(e^jw) = B / A, where A
= 1; and B consists of some higer ordered polynomial
> 2). If IIR filter is having such instability issues..then why do
we use IIR filters.??
You can design around the instabilities, they are often used in
audio applications, because they can have linear phase over a
channel, as well as a solid response, so they are advantagious.

> 3). In which applications.. do we use an IIR filter???
Audio, noise cancelation, real time processing where memory and
hardware cost is important.
> 4). Which is a better equalizer...FIR or IIR?
FIR, but is more complicated, typically you need a multirate scheme
to be able to use FIR filters effienciently
> 5). Is there any condition..when an IIR filter can act as a LINEAR
> FILTER?
why yes, see above, and see the MITRA book, there is a detailed
explanation in it, you can also check out www.dspguru.com for some
more information. And ask questions on here that are more specific.



mu suggestion would be that you pick look through oppenheim & schaefer's
"discrete-time signal processing" to get proper grounding on linearity,
causality, stability, etc because it appears that you may be confusing
some of these terms in your beliefs.

a couple of points to note:

- not all fir filters are linear phase. daubechies orthonormal wavelet
filters are a good examples
- not all iir filters are not linear phase; look at the phase response of
any filter generated by the 'butter' function in matlab.

--- utd_anurag <> wrote:

> Hi,
> I am new to this group.
> I want to initiate a discussion pertaining to FIR and IIR filters.
> I am adding my beliefs & have a few questions.

>
> 1). Is FIR an all-zero/all-pole/mixed filter?
> 2). If IIR filter is having such instability issues..then why do we
> use IIR filters.??
> 3). In which applications.. do we use an IIR filter???
> 4). Which is a better equalizer...FIR or IIR?
> 5). Is there any condition..when an IIR filter can act as a LINEAR
> FILTER?


=====

__________________________________


Chatonda-

> mu suggestion would be that you pick look through oppenheim & schaefer's
> "discrete-time signal processing" to get proper grounding on linearity,
> causality, stability, etc because it appears that you may be confusing
> some of these terms in your beliefs.
>
> a couple of points to note:
>
> - not all fir filters are linear phase. daubechies orthonormal wavelet
> filters are a good examples

Good point. As well, a linear phase FIR filter can be converted to "minimum
phase",
in which case it has the exact same magnitude response as the original, but its
phase
is definitely no longer linear.

-Jeff




Anurag-

> 3). In which applications.. do we use an IIR filter???

There are some applications where the usage of FIR filters is simply not
practical.
Put another way, some applications where only reasonable amount of
processing power is available but a very high degree of filtering is
required can be solved only by using IIR filters. They are more *realizable*
than FIR filters in some situations.

Assume this situation and see if you can design a (practical!) FIR filter
for the same:

Problem Defintion:
--------------------------
To do filtering on a certain signal- a sine wave consisting of three
different frequency ranges. ie, in real-time the signal could consist of
any 3 frequencies of the folllowing nature-

1]any one particular frequency in the range 9.5-16.5hz
2]any one particular frequency in the range 19-31hz
3]any one particular frequency in the range 38-62hz

The signal that *passes* through your filter should be a combination of
three frequencies out of these three *boxes* only!

Assume also that the required frequency resolution is .5hz. I.e i need to do
know the difference between 9.5hz and 10.0 hz. Exactly.

Assume, available processing power: 50 MIPS!

Design the filter as both IIR and FIR and see which is more practical.As a
simple thumb rule, if the order of the filter is greater than 5 or
10...forget it!

Points to Poinder:
------------------------
1] So,the maximum frequency is not more than 100hz
2] My signal of interest could be 25hz,40hz and 12hz the first time and
30hz,50hz and 10hz the next time and so on...if so, they should be
passed...otherwise they should be rejected

Caution:
-----------
Your filter should pass 10.5 hz but should *not* pass 17.5hz, your filter
should pass 20 hz but *should not pass* 32 hz etc...

Not a valid solution:
--------------------------
A pass-band filter of range,say, 8hz-80hz(which covers all the 3 ranges i
mentioned above...)

Why?
--------
Figure out.

Hints:
------
1] The desired filter passbands are centered at 2:1 frequency multiples
2] Are they octaves apart?
3] Paramteric Eq's?

Finally, Is the solution elliptical in nature?

--Bhooshan.N.Iyer

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