Here is a schematic of my desired circuit. enter image description here

I want to calculate Power and Energy that the load dissipates during 0< t<8 You can see my attempts:

scan of sheet Therefore

  1. How can find load's energy in Frequency domain for desired time domain interval (0 < t < 8) ?
  2. Did I obtain power correctly in frequency domain?
  • $\begingroup$ Are you sure you have written the question correctly? It seems like $H(f)=1$ probably for $|f|<f_0$ and $H(f)=0$ otherwise. It is somehow meaningless at the moment. $\endgroup$
    – msm
    Commented Dec 5, 2016 at 9:03
  • $\begingroup$ Thanks for your response.Actually I think my system is an Ideal wire where y(t)=x(t) and h(t) should be equal to delta function $\endgroup$ Commented Dec 5, 2016 at 9:50

1 Answer 1


The relationships, with $x$ the input voltage to the network, $y$ the output voltage from the network, $R$ the load resistance, $p(t)$ the instantaneous power dissipated at the load, and $E$ the energy dissipated at the load and $t_0=8$

$$Y(f)=H(f)X(f)\\ y(t)=\mathscr{F}^{-1}\{Y(f)\}\\ p(t)=\frac{y^2(t)}{R}\\E\bigg|_{t=0}^{t_0}=\int_0^{t_0}p(t)dt=\int_0^{t_0}\frac{y^2(t)}{R} dt$$

IF the cable or network is a lossless cable (!), the example turns trivial: $$y(t)=x(t)\\ p(t)=\frac{x^2(t)}{R}\\ E\bigg|_{t=0}^{t_0}=\int_0^{t_0}\frac{x^2(t)}{R} dt$$

  • $\begingroup$ Thanks hypfco for your contribution and response ,as you can see in the first section of my attempts I use your equation to obtain Energy in time domain but my question is how can find Energy in frequency domain while 0 < t<8 , is it possible without going to time domain obtain Energy in frequency domain for specific time duration ? and was my attempts correct to obtain power in frequency domain? $\endgroup$ Commented Dec 5, 2016 at 13:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.