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?
Theory 101 - Impulse response of "perfect" LPF
Started by ●December 12, 2006
Reply by ●December 12, 20062006-12-12
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. �����������������������������������������������������������������������
Reply by ●December 12, 20062006-12-12
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
Reply by ●December 12, 20062006-12-12
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. �����������������������������������������������������������������������
Reply by ●December 12, 20062006-12-12
>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.
Reply by ●December 12, 20062006-12-12
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
Reply by ●December 12, 20062006-12-12
>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.
Reply by ●December 12, 20062006-12-12
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. �����������������������������������������������������������������������
Reply by ●December 12, 20062006-12-12
"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 Reverse name to reply
Reply by ●December 12, 20062006-12-12
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
