Filter Output Energy

If a signal with energy 'E' is filtered with a filter having unit energy,
what is the energy of the output signal?
Thanks.

On Oct 18, 5:53&#4294967295;am, "commsignal" <commsignal@n_o_s_p_a_m.yahoo.com>
wrote:
> If a signal with energy 'E' is filtered with a filter having unit energy,
> what is the energy of the output signal?

mind telling us what it means for a filter to have unit energy?  a
filter is a device, not a signal.  i can tie together an resistor and
capacitor and call it a filter.  if you know R and C, can you tell me
what the filter's energy is?

r b-j

On Oct 18, 5:53&#4294967295;am, "commsignal" <commsignal@n_o_s_p_a_m.yahoo.com>
wrote:
> If a signal with energy 'E' is filtered with a filter having unit energy,
> what is the energy of the output signal?
> Thanks.

Exercise: The signal is sqrt{2E} cos(2*pi*1000*t),
a signal of energy E at 1 kHz. it is passed through
a bandpass filter with center frequency 100 MHz
and bandwidth 1 MHz.  What do you think is the
energy of the output signal?

Assuming that "filter having unit energy" means that
the impulse response of the filter is a unit-energy signal,
all that can be said that the output signal will have
energy _at most_ E, and this extreme value will occur
if the filter is matched to the signal.

Dilip Sarwate

On Tue, 18 Oct 2011 05:46:21 -0700, robert bristow-johnson wrote:

> On Oct 18, 5:53&nbsp;am, "commsignal" <commsignal@n_o_s_p_a_m.yahoo.com>
> wrote:
>> If a signal with energy 'E' is filtered with a filter having unit
>> energy, what is the energy of the output signal?
> 
> mind telling us what it means for a filter to have unit energy? 

Maybe it means that if you run out of wood pellets for your stove that 
you can toss in the filter to keep a unit house warm for a unit time?


-- 
www.wescottdesign.com

On Tue, 18 Oct 2011 08:37:22 -0700, dvsarwate wrote:

> On Oct 18, 5:53&nbsp;am, "commsignal" <commsignal@n_o_s_p_a_m.yahoo.com>
> wrote:
>> If a signal with energy 'E' is filtered with a filter having unit
>> energy, what is the energy of the output signal? Thanks.
> 
> Exercise: The signal is sqrt{2E} cos(2*pi*1000*t), a signal of energy E
> at 1 kHz. it is passed through a bandpass filter with center frequency
> 100 MHz and bandwidth 1 MHz.  What do you think is the energy of the
> output signal?
> 
> Assuming that "filter having unit energy" means that the impulse
> response of the filter is a unit-energy signal, all that can be said
> that the output signal will have energy _at most_ E, and this extreme
> value will occur if the filter is matched to the signal.

Since Dilip appears to have done your homework for you, will he get your 
grade?

-- 
www.wescottdesign.com

On Oct 18, 12:30&#4294967295;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On Tue, 18 Oct 2011 05:46:21 -0700, robert bristow-johnson wrote:
> > On Oct 18, 5:53&#4294967295;am, "commsignal" <commsignal@n_o_s_p_a_m.yahoo.com>
> > wrote:
> >> If a signal with energy 'E' is filtered with a filter having unit
> >> energy, what is the energy of the output signal?
>
> > mind telling us what it means for a filter to have unit energy?
>
> Maybe it means that if you run out of wood pellets for your stove that
> you can toss in the filter to keep a unit house warm for a unit time?

:-)

well, i burn split wood (or i will when it gets a little colder),
kerosene (or #2 fuel oil), or the potential energy stored up in
electrons.  the oil furnace has a filter, dunno what its heating
output is if i burn it.

BTW, yesterday i got to do a little local volunteering to help with
Hurricane Irene relief in more central Vermont.  this is a strange
state.  i helped this 61 YO guy who, along with wife and son (who is
the chef), owns a restaurant in Waitsfield that got whacked by the
raging Mad River.  i have no doubt that this guy (or his family) is
likely worth 7 digits (which, these days is less impressive than it
was during the Beverly Hillbilly days), yet he was making deals with
other locals for excess 3/4" plywood (at $5 per 4x8 sheet), and i was
helping this guy load, transport, and unload this and also a few
thousand dollars of paint that folks in the town is sharing.  (i was
doing this while waiting for my laptop Mac to get fixed.)

it was a sorta good catharsis because last June and July, i was the
recipient of similar volunteer help.  you can see a sorta graphical
chronology of both events at http://waterdata.usgs.gov/vt/nwis/dv/?site_no=04294500
.  the latest step function (just before Sept 1) is the result of
Irene, the lake rose 2 feet in 48 hours, but that was nothing compared
to what happened with these little rivers that suddenly became big
rivers.

the sense of community and shared experience (both the good and the
bad) is like no other place i lived in, including my stomping ground
of North Dakota.  Vermont is like no other state in the country.  i
probably should not be revealing our "little secret" shared by the
other 600K residents of the state.

r b-j

On 10/18/2011 11:37 AM, dvsarwate wrote:
> On Oct 18, 5:53 am, "commsignal"<commsignal@n_o_s_p_a_m.yahoo.com>
> wrote:
>> If a signal with energy 'E' is filtered with a filter having unit energy,
>> what is the energy of the output signal?
>> Thanks.
>
> Exercise: The signal is sqrt{2E} cos(2*pi*1000*t),
> a signal of energy E at 1 kHz. it is passed through
> a bandpass filter with center frequency 100 MHz
> and bandwidth 1 MHz.  What do you think is the
> energy of the output signal?
>
> Assuming that "filter having unit energy" means that
> the impulse response of the filter is a unit-energy signal,
> all that can be said that the output signal will have
> energy _at most_ E, and this extreme value will occur
> if the filter is matched to the signal.

A real stumper for many beginners is, "If the energy doesn't come out of 
the filter, where does it go?" There's no problem with digital filters. 
After all, it's merely numbers. But what about analog filters made of 
lossless components?

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

On Oct 18, 1:48&#4294967295;pm, Jerry Avins <j...@ieee.org> wrote:

>
> A real stumper for many beginners is, "If the energy doesn't come out of
> the filter, where does it go?" There's no problem with digital filters.
> After all, it's merely numbers. But what about analog filters made of
> lossless components?
>


So here is a question about analog lossless components.
A capacitor C is charged to V volts and thus is storing energy
0.5CV^2.  It is connected in parallel to an identical capacitor
through lossless (zero-resistance) wires, and so charge flows
from one capacitor to the other till each capacitor is holding
half the charge and thus has voltage V/2 across it.  Now the
energy being stored is 0.5C(V/2)^2 + 0.5C(V/2)^2 = 0.25CV^2.
What happened to the rest of the energy?

--Dilip Sarwate

P.S.  Answers of E = mc^2 will receive zero credit!

http://www.masslive.com/news/index.ssf/2011/08/in_vermont_town_cut_off_after_hurricane_irene_flooding.html

http://www.valleyreporter.com/index.php?option=com_content&task=view&id=4177&ac=0&Itemid=38

On 10/18/2011 2:00 PM, dvsarwate wrote:
> On Oct 18, 1:48 pm, Jerry Avins<j...@ieee.org>  wrote:
>
>>
>> A real stumper for many beginners is, "If the energy doesn't come out of
>> the filter, where does it go?" There's no problem with digital filters.
>> After all, it's merely numbers. But what about analog filters made of
>> lossless components?
>>
>
>
> So here is a question about analog lossless components.
> A capacitor C is charged to V volts and thus is storing energy
> 0.5CV^2.  It is connected in parallel to an identical capacitor
> through lossless (zero-resistance) wires, and so charge flows
> from one capacitor to the other till each capacitor is holding
> half the charge and thus has voltage V/2 across it.  Now the
> energy being stored is 0.5C(V/2)^2 + 0.5C(V/2)^2 = 0.25CV^2.
> What happened to the rest of the energy?
>
> --Dilip Sarwate
>
> P.S.  Answers of E = mc^2 will receive zero credit!

I won't give it away, but instead pose a mechanical version. Two 
identical flywheels, moment of inertia I, can be coupled by a dog 
clutch. Initially, one rotates at angular velocity w radians/second and 
the other is stationary. Without exerting any forces outside of the 
system, the flywheels are coupled by the dog clutch. Momentum being 
conserved, they then rotate together at w/2. Before they were coupled, 
the total energy was 0.5Iw^2, all in the rotating part. After the 
coupling, the energy of the flywheels together is 0.5(2I)(w/2)^2, or 
0.25Iw^2. What happened to the rest of the energy?

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