The energy of a signal is defined as
, oo
Ef = | (|f(t)|)^2 dt
,-oo
It seems that this signal is evaluated over all time. If I want to find
the energy at time t, would I simply integrate over a short time
interval? Maybe like the following?
, t+pi/w
Ef = | (|f(t)|)^2 dt
, t-pi/w
Energy Density at Time t
Started by ●April 11, 2007
Reply by ●April 11, 20072007-04-11
On Apr 11, 10:07 am, Chris Barrett <"chrisbarret"@0123456789abcdefghijk113322.none> wrote:> The energy of a signal is defined as > > , oo > Ef = | (|f(t)|)^2 dt > ,-oo > > It seems that this signal is evaluated over all time. If I want to find > the energy at time t, would I simply integrate over a short time > interval? Maybe like the following? > > , t+pi/w > Ef = | (|f(t)|)^2 dt > , t-pi/wHello Chris, Yes energy is simply integral of |f(t)|^2 dt over all space. Your energy density is simply |f(t)|^2 Your mean power is integral from t1 to t2 of |f(t)|^2 dt / (t2-t1) IHTH, Clay
Reply by ●April 11, 20072007-04-11
Chris Barrett wrote:> The energy of a signal is defined as > > , oo > Ef = | (|f(t)|)^2 dt > ,-oo > > It seems that this signal is evaluated over all time.It seems? It explicitly states! (What is the absolute value for? Can f(t) be a complex function?)> If I want to find > the energy at time t, would I simply integrate over a short time > interval? Maybe like the following? > > , t+pi/w > Ef = | (|f(t)|)^2 dt > , t-pi/wEnergy is the integral of power over time. The energy at time t is zero, whatever the power may be. Your expression represents the energy in an interval 2pi/w centered about time t. Is that what you want? Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 11, 20072007-04-11
Jerry Avins wrote:> Chris Barrett wrote: > >> The energy of a signal is defined as >> >> , oo >> Ef = | (|f(t)|)^2 dt >> ,-oo >> >> It seems that this signal is evaluated over all time. > > > It seems? It explicitly states! (What is the absolute value for? Can > f(t) be a complex function?) > >> If I want to find the >> energy at time t, would I simply integrate over a short time interval? >> Maybe like the following? >> >> , t+pi/w >> Ef = | (|f(t)|)^2 dt >> , t-pi/w > > > Energy is the integral of power over time. The energy at time t is zero, > whatever the power may be. Your expression represents the energy in an > interval 2pi/w centered about time t. Is that what you want? > > JerryYes. I have a signal of constant frequency and varying amplitude.
Reply by ●April 11, 20072007-04-11
On 11 Apr, 20:52, Chris Barrett <"chrisbarret"@0123456789abcdefghijk113322.none> wrote:> Jerry Avins wrote: > > Your expression represents the energy in an > > interval 2pi/w centered about time t. Is that what you want? > > > Jerry > > Yes. I have a signal of constant frequency and varying amplitude.- Skjul sitert tekst -An AM signal? Would an envelope detector be useful to you? Rune
Reply by ●April 12, 20072007-04-12
On Apr 11, 11:03 am, Jerry Avins <j...@ieee.org> wrote:> Chris Barrett wrote: > > The energy of a signal is defined as > > > , oo > > Ef =3D | (|f(t)|)^2 dt > > ,-oo > > > It seems that this signal is evaluated over all time. > > It seems? It explicitly states! (What is the absolute value for? Can > f(t) be a complex function?) > > > If I want to find > > the energy at time t, would I simply integrate over a short time > > interval? Maybe like the following? > > > , t+pi/w > > Ef =3D | (|f(t)|)^2 dt > > , t-pi/w > > Energy is the integral of power over time. The energy at time t is zero, > whatever the power may be. Your expression represents the energy in an > interval 2pi/w centered about time t. Is that what you want? > > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF==AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF Hello Jerry, One case of where I see f(t) as a complex function is in a description of E-M waves. Think about a plane wave moving along the positive x-axis, it is written as E(x,t)=3DE * exp(ikx - iwt) and the constant E may be complex Thus E*(x,t)E(x,t) =3D |E|^2 If using mks units, the total energy density (power/volume) =3D epsilon_0*|E|^2 By total energy I've already included the magnetic energy as well since the two are linked. E=3DcB. Clay
Reply by ●April 12, 20072007-04-12
On 12 Apr., 16:07, "Clay" <phys...@bellsouth.net> wrote:> On Apr 11, 11:03 am, Jerry Avins <j...@ieee.org> wrote: > > > > > > > Chris Barrett wrote: > > > The energy of a signal is defined as > > > > , oo > > > Ef =3D | (|f(t)|)^2 dt > > > ,-oo > > > > It seems that this signal is evaluated over all time. > > > It seems? It explicitly states! (What is the absolute value for? Can > > f(t) be a complex function?) > > > > If I want to find > > > the energy at time t, would I simply integrate over a short time > > > interval? Maybe like the following? > > > > , t+pi/w > > > Ef =3D | (|f(t)|)^2 dt > > > , t-pi/w > > > Energy is the integral of power over time. The energy at time t is zero, > > whatever the power may be. Your expression represents the energy in an > > interval 2pi/w centered about time t. Is that what you want? > > > Jerry > > -- > > Engineering is the art of making what you want from things you can get. > > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF==AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF> > Hello Jerry, > > One case of where I see f(t) as a complex function is in a description > of E-M waves.Any waves, really. f(t) could be the Fourier transform of some finite- energy signal, in which case the truncated integral measures the energy contained in a frequency band. Regards, Andor
Reply by ●April 12, 20072007-04-12
Clay wrote:> On Apr 11, 11:03 am, Jerry Avins <j...@ieee.org> wrote:...>> Can f(t) be a complex function?...> One case of where I see f(t) as a complex function is in a description > of E-M waves.... Thanks, Clay. I should have written "Can f(t) be a complex function in your case?" I couldn't distinguish between the OP's desire to cite the most general case and his blindly citing an equation without troubling to read meaning into it. I hoped I might be prodding him to think. That's probably presumptuous of me, but it seemed to go along with his seeking an expression for energy at a particular instant. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 12, 20072007-04-12
On Apr 12, 11:32 am, Jerry Avins <j...@ieee.org> wrote:> Clay wrote: > > On Apr 11, 11:03 am, Jerry Avins <j...@ieee.org> wrote: > > ... > > >> Can f(t) be a complex function? > > ... > > > One case of where I see f(t) as a complex function is in a description > > of E-M waves. > > ... > > Thanks, Clay. I should have written "Can f(t) be a complex function in > your case?" I couldn't distinguish between the OP's desire to cite the > most general case and his blindly citing an equation without troubling > to read meaning into it. I hoped I might be prodding him to think. > > That's probably presumptuous of me, but it seemed to go along with his > seeking an expression for energy at a particular instant. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF==AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF Jerry, it is no problem. Since many questions posed here are often supported with little to no information, we all have to guess/surmise what the original poster is asking and more importantly their framework from which the question arises. I know many times the assumptions I make turn out to be not applicable to the OP's question after the OP has qualified the question with additional details. Clay
Reply by ●April 12, 20072007-04-12
On Apr 12, 10:19 am, "Andor" <andor.bari...@gmail.com> wrote:> On 12 Apr., 16:07, "Clay" <phys...@bellsouth.net> wrote: > > > > > > > On Apr 11, 11:03 am, Jerry Avins <j...@ieee.org> wrote: > > > > Chris Barrett wrote: > > > > The energy of a signal is defined as > > > > > , oo > > > > Ef =3D | (|f(t)|)^2 dt > > > > ,-oo > > > > > It seems that this signal is evaluated over all time. > > > > It seems? It explicitly states! (What is the absolute value for? Can > > > f(t) be a complex function?) > > > > > If I want to find > > > > the energy at time t, would I simply integrate over a short time > > > > interval? Maybe like the following? > > > > > , t+pi/w > > > > Ef =3D | (|f(t)|)^2 dt > > > > , t-pi/w > > > > Energy is the integral of power over time. The energy at time t is ze=ro,> > > whatever the power may be. Your expression represents the energy in an > > > interval 2pi/w centered about time t. Is that what you want? > > > > Jerry > > > -- > > > Engineering is the art of making what you want from things you can ge=t=2E> > > =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF==AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF> > > Hello Jerry, > > > One case of where I see f(t) as a complex function is in a description > > of E-M waves. > > Any waves, really. f(t) could be the Fourier transform of some finite- > energy signal, in which case the truncated integral measures the > energy contained in a frequency band. > > Regards, > Andor- Hide quoted text - >Hello Andor, I was just giving an example. Sometimes the magnitude squared thing seems a little foreign, but as you mention, it turns out to be quite universal. I know I use it all of the time in quantum mechanics problems. I'm up to my ears in atomic structure calculations these days. Clay
