# find power of the signal

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:

$Y(f)=X(f)H(f)$.

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

$C_n=1$

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

• 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. – Laurent Duval Apr 14 '17 at 10:23
• your $\sum$ symbol is direly missing limits – that makes the difference whether this question is answerable at all or not. – Marcus Müller Apr 14 '17 at 17:24

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?