# Theory 101 - Impulse response of "perfect" LPF

Started by December 12, 2006
```OK, I'm going to really stick my naive neck out on this one...

Why isn't the impulse response of a perfect LPF a flat line (i.e., zero)?

For example, an infinitely large mass (the filter) hit by an infinitely
small particle (the impulse) would not move at all because of its inertia
(acceleration goes to zero as masses go to +/-infinity).

So why is the impulse response of an infinitely long (perfect) LP FIR a
"sinc" function rather than zero?
```
```jeff227 wrote:
> OK, I'm going to really stick my naive neck out on this one...
>
>
> Why isn't the impulse response of a perfect LPF a flat line (i.e., zero)?
>
> For example, an infinitely large mass (the filter) hit by an infinitely
> small particle (the impulse) would not move at all because of its inertia
> (acceleration goes to zero as masses go to +/-infinity).
>
> So why is the impulse response of an infinitely long (perfect) LP FIR a
> "sinc" function rather than zero?

You are imagining the wrong model. A mass is not a "perfect LPF", one
whose response constant up to some frequency and zero at higher ones.
It's no surprise that an analogiy based on a flawed model yields a
flawed conclusion.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```jeff227 skrev:
> OK, I'm going to really stick my naive neck out on this one...
>
>
> Why isn't the impulse response of a perfect LPF a flat line (i.e., zero)?

Because of the "P" in LPF.

> So why is the impulse response of an infinitely long (perfect) LP FIR a
> "sinc" function rather than zero?

It pops directly out from applying the IFFT to the definition of a
perfect LPF as expressed in frequency domain.

Rune

```
```Rune Allnor wrote:
> jeff227 skrev:
>> OK, I'm going to really stick my naive neck out on this one...
>>
>>
>> Why isn't the impulse response of a perfect LPF a flat line (i.e., zero)?
>
> Because of the "P" in LPF.
>
>> So why is the impulse response of an infinitely long (perfect) LP FIR a
>> "sinc" function rather than zero?
>
> It pops directly out from applying the IFFT to the definition of a
> perfect LPF as expressed in frequency domain.

Sure. As far as I can see, what Jeff wanted is not a proof, but an
explanation for his intuition being wrong.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```>Jerry
>You are imagining the wrong model...
>It's no surprise that an analogiy based on a flawed model yields a
>flawed conclusion.

OK, got it.  However I believe this "mass model" analogy IS correct - it
has an Fc of zero.  "Sinc" of Fc zero is zero.

Useless information - just trying to gain an understanding of principles.

Thank you for the replies.
```
```jeff227 skrev:
> OK, I'm going to really stick my naive neck out on this one...
>
>
> Why isn't the impulse response of a perfect LPF a flat line (i.e., zero)?
>
> For example, an infinitely large mass (the filter) hit by an infinitely
> small particle (the impulse) would not move at all because of its inertia
> (acceleration goes to zero as masses go to +/-infinity).

This has no relevance to LPFs. This corresponds to exciting
the system with an impulse with vanishingly small amplitude.

> So why is the impulse response of an infinitely long (perfect) LP FIR a
> "sinc" function rather than zero?

It would be, if the impulse has zero amplitude.

Rune

```
```>This has no relevance to LPFs.

Wrong!  A spring, damper and mass is EXACTLY equivalent to a LPF.  In this
example the spring and damper are zero and the mass is infinite.

Before you insult my intelligence take some time to think outside the
box.

```
```jeff227 wrote:

> OK, got it.  However I believe this "mass model" analogy IS correct - it
> has an Fc of zero.  "Sinc" of Fc zero is zero.

Not correct. The mass integrates the impulse, and after it is applied,
moves at constant velocity.  Your perfect LPF responds without
attenuation to any frequency below cutoff, and not at all to any
frequency above. No finite mass responds that way. Passing to a limit
shouldn't introduce new behavior.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```"jeff227" <rocksonics@earthlink.net> wrote in news:8cidnVYW8O0zR-
PYnZ2dnUVZ_hm3nZ2d@giganews.com:

> infinitely small particle (the impulse)

An impulse is not infinitely small, just infinitely narrow.  Still
integrates to one.  In fact, you can say its infinitely small in one
dimensin, but infinitely big in the other.

--
Scott
```
```jeff227 skrev:
> >This has no relevance to LPFs.
>
>
> Wrong!  A spring, damper and mass is EXACTLY equivalent to a LPF.

It is a mechanical analogy, yes.

> In this
> example the spring and damper are zero and the mass is infinite.

It is up to you to justify why the analogy would still hold, and
that it is relevant to the example you try to discuss.

> Before you insult my intelligence take some time to think outside the
> box.

If anybody insult your intelligence, it is you. I fail to see
why an example that involves "infinitely small" and "infinitely
large" quantities should remain relevant as an analogy
for anything.

If you want to think outside the "box" you apparently try to
break out of yourself, just keep in mind that every single
word in a problem specification has a meaning, and influence
the way to treat the problem. Remove the two instances
of the word "infinitely" in your stated problem, and you
will have a completely different discussion. An intelligent
debattante will see that. Do you?

Rune

```