FPGA Central

Hello Forum,

what is the main difference between infinite impulse response and finit
impulse response filters?
Clearly, in real life, all filters should have a finite response: after
while the response must die off.

In digital processing, a FIR is also necessary since we deal with finit
amounts of data....

So, what is the point of a IIR filter? Any example? Is it just an analo
theoretical concept? Surely a Gaussian dies off to zero only at infinity b
the area under it is finite.....

thanks
fisico32

On Nov 11, 12:08*pm, "fisico32" <marcoscipio...@gmail.com> wrote:
> Hello Forum,
>
> what is the main difference between infinite impulse response and finite
> impulse response filters?
> Clearly, in real life, all filters should have a finite response: after a
> while the response must die off.
>
> In digital processing, a FIR is also necessary since we deal with finite
> amounts of data....
>
> So, what is the point of a IIR filter? Any example? Is it just an analog
> theoretical concept? Surely a Gaussian dies off to zero only at infinity by
> the area under it is finite.....
>
> thanks
> fisico32

IIR filters do have an impulse response that is infinite in duration.
You're right that most IIR filters have an impulse response that
decays to zero over time, and at some point, the response will decay
below 1 LSB of precision if you're using fixed point. From an
engineering perspective, for these examples and other "analog"
situations, there often comes a point in time where the response
decays to a point where it is negligible, although they are
mathematically modeled as being infinite in duration.

However, there are some IIR filters that don't decay to zero; consider
a system with a pole on the unit circle; its impulse response is a
sinusoid, whose frequency depends on where the pole lies.

Jason

On Nov 11, 11:08*am, "fisico32" <marcoscipio...@gmail.com> wrote:
> Hello Forum,
>
> what is the main difference between infinite impulse response and finite
> impulse response filters?
> Clearly, in real life, all filters should have a finite response: after a
> while the response must die off.
>
> In digital processing, a FIR is also necessary since we deal with finite
> amounts of data....
>
> So, what is the point of a IIR filter? Any example? Is it just an analog
> theoretical concept? Surely a Gaussian dies off to zero only at infinity by
> the area under it is finite.....
>
> thanks
> fisico32

IIR filters are not mere theory. They are often used when linear phase
response is not required and the desired magnitude response would
require a much longer FIR filter than IIR filter.

Darol Klaweter

fisico32 wrote:
> Hello Forum,
>
> what is the main difference between infinite impulse response and finite
> impulse response filters?
> Clearly, in real life, all filters should have a finite response: after a
> while the response must die off.
>
> In digital processing, a FIR is also necessary since we deal with finite
> amounts of data....
>
> So, what is the point of a IIR filter? Any example? Is it just an analog
> theoretical concept? Surely a Gaussian dies off to zero only at infinity by
> the area under it is finite.....

The impulse response of a filter doesn't determine how much data can be
run through it. You ought to learn what these structures are, rather
than asking about differences between things you don't understand. Read
up about them on http://dspguide.com/, Wikipadia, and
http://www.bores.com/courses/intro/index.htm

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

"fisico32" <[email protected]> writes:

> Hello Forum,
>
> what is the main difference between infinite impulse response and finite
> impulse response filters?
> Clearly, in real life, all filters should have a finite response: after a
> while the response must die off.
>
> In digital processing, a FIR is also necessary since we deal with finite
> amounts of data....
>
> So, what is the point of a IIR filter? Any example? Is it just an analog
> theoretical concept? Surely a Gaussian dies off to zero only at infinity by
> the area under it is finite.....

First you should separate the real-world from theory. There are no
infinitely-precise real numbers in the real world either - does that
mean they're not useful?

They are significantly different, besides the impulse response. IIR has
only poles (except for zeros at 0), while FIR has only zeros (except for
poles at 0). Also an IIR is inherently based on feedback, while an FIR
is not (necessarily).
--
Randy Yates % "And all you had to say
Digital Signal Labs % was that you were
mailto://[email protected] % gonna stay."
http://www.digitalsignallabs.com % Getting To The Point', *Balance of Power*, ELO

Randy Yates <[email protected]> writes:
> [...]
> IIR has only poles (except for zeros at 0),

Wups. This was wrong - too quick of a response.

An IIR has non-trivial poles (it could have non-trivial zeros as well).
--
Randy Yates % "She tells me that she likes me very much,
Digital Signal Labs % but when I try to touch, she makes it
mailto://[email protected] % all too clear."
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO

On Wed, 11 Nov 2009 11:08:34 -0600, fisico32 wrote:

> Hello Forum,
>
> what is the main difference between infinite impulse response and finite
> impulse response filters?
> Clearly, in real life, all filters should have a finite response: after
> a while the response must die off.

Clearly, in real life, some filters should _not_ have a finite response:
the integrator in a PID controller needs to have a sustained, non-zero
response to a zero input to hold the process output at a desired DC value
even when process needs a non-zero input to do so.

> In digital processing, a FIR is also necessary since we deal with finite
> amounts of data....

In digital processing we often deal with data that is practically
infinite. Consider a digital cell phone, which uses DSP to decode the
data that's turned into the sounds that you hear. Do you want a phone
that stops working any time it gets 5 minutes into a call? 10 minutes?
One hour? No, you don't want it to _ever_ stop because 'the input data
is finite'. You want it to keep going, and going and going.

FIR filters are _handy_ for a variety of reasons (and are used heavily in
a cell phone type demod application), but not because of that.

> So, what is the point of a IIR filter?

To provide and infinitely long response where it is needed, or to provide
desired filtering where the phase vs. amplitude characteristics of an IIR
filter are negligible or desirable.

> Any example?

PID controllers.

Any place where filtering with a cut-off frequency much lower than the
sample rate is desired, and same phase distortion can be tolerated (or,
in the case of a control loop, where a minimum phase filter is necessary).

> Is it just an analog theoretical concept?

No. The world is full of real systems that have infinitely long
responses to real events. Fire, flood, plagues and drought are hardly
remote theoretical concepts when you're caught up in one.

> Surely a Gaussian dies off to zero only at infinity
> by the area under it is finite.....

Yea, so?

--
www.wescottdesign.com

On Nov 11, 5:08*pm, "fisico32" <marcoscipio...@gmail.com> wrote:
> Hello Forum,
>
> what is the main difference between infinite impulse response and finite
> impulse response filters?
> Clearly, in real life, all filters should have a finite response: after a
> while the response must die off.
>
> In digital processing, a FIR is also necessary since we deal with finite
> amounts of data....
>
> So, what is the point of a IIR filter? Any example? Is it just an analog
> theoretical concept? Surely a Gaussian dies off to zero only at infinity by
> the area under it is finite.....

1) An IIR filter can achieve, for example, a given frequency domain
cutoff with less computation (coefficients) than an FIR.

2) An IIR filter can readily duplicate the response of an analog
filter - and so for example may be used where such a filter is
required either according to a standard or to duplicate the
performance of an analog system that is being replaced by a digital
implementation.

3) An IIR filter can have an impulse response that is infinite, which
is useful when you want the impusle response to be infinite (for
example to build an oscillator).

Chris
===========
Chris Bore
BORES Signal Processing
www.bores.com


>
> thanks
> fisico32