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diredragon

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## Homework Statement

The input signal of the circuit shown below is ##x(t)=2\sin (ω_ot + \pi/6)##. The switch in the circuit is controlled with a digital signal of the form ##s(t)=\sum_{k=-\infty}^{+\infty} (u(t+ε-kT_s) - u(t-ε-kT_s))##, ##\frac{2\pi}{T_s}=800\pi##, ##ε\to 0##, so that when the signal equals 1 the switch is in the position 1 (closed).

a) Calculate ##X_s(jω)##

b) If ##g[n]=x_s(nT_s + 0.3T_s)## calculate ##G(jΩ)##.

Note: ##u(t)## is a step funtion, defined as ##u(0)=\frac{1}{2}##

## Homework Equations

3. The Attempt at a Solution [/B]

I am not sure how to start and what to do with this digital signal that's controlling the switch. It looks like a sum of delta impulses with very narrow width of ##ε## and a period of ##T_s##. My first thought was that this was some sort of sampling circuit and that i should do a convolution of the two signals to find the ##X_s(jω)##. Something like this:

##x_s(t)=x(t)*s(t)##

##X_s(jω)=\mathscr{L}\{x(t)\} \mathscr{L}\{s(t)\}##. Is this the correct approach?

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