I have this signal: $$x(t)=\sum \mathrm{rect}\left(\frac {t-kT_0} {20}\right)+\mathrm{rect}\left(\frac {t-kT_0} {40}\right)+\mathrm{rect}\left(\frac {t-kT_0} {80}\right)$$ with $T_0=140$, pass it through the filter $H(f)={\mathrm{rect}}\left(\frac f F\right)$. What is the value of $F$ such that power is $P=1$?

Fourier Trasform is:

$\sum C_n\delta(f-nf_0)$

$C_n=\frac 1 {T_0}[sinc(20nf_0)+sinc(n40f_0)+sinc(n80f_0)]$

if call y(t) the signal output, I have:


the power spectral density is:

$P(f)= \sum (|C_n|^2\delta(f-nf_0))|H(f)|^2$

with $P_x(f)=\sum (|C_n|^2\delta(f-nf_0) $

don't know find F

if don't error for n=0


so for $0<F<\frac 1 {T_0}$ the power should be 1. but I'don't sure

  • 1
    $\begingroup$ Welcome to SE.DSP. The question looks like homework. The community will be more likely to help you if you provide the first steps of your reasoning, and where you are blocked. BTW, "con" is probably "with. $\endgroup$ Commented Apr 14, 2017 at 10:23
  • $\begingroup$ your $\sum$ symbol is direly missing limits – that makes the difference whether this question is answerable at all or not. $\endgroup$ Commented Apr 14, 2017 at 17:24

1 Answer 1


Since this is clearly homework, and the limits on the $\sum$ are crucial to figuring out whether there's an answer:

Hint: Parseval's Theorem states that power in time domain is equivalent to power in frequency domain. What is the power in $x(t)$? Is $x(t)$ periodic? If so, what's the period?

As usual, it often helps to make a drawing (that's, by the way, the minimum I'd have expected from your question!) to get a feeling for the signal you're dealing with.


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.