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## Homework Statement

Consider the signal [tex]x(t)=cos(4t)+cos(5t)+cos(6t)[/tex], and the SLIT with impulse response:

[tex]h(t)=\begin{cases} 1, & \mbox{if } |t|<T \\ 0, & \mbox{if } |t|>T \end{cases}[/tex]

For what value of T is the output of the system [tex] y(t) [/tex] equal to [tex]Acos(4t)+Bcos(5t)[/tex], when [tex]x(t)[/tex] is the input?

## The Attempt at a Solution

I know that this can be solved through Fourier Transform and the solution is [tex]T=\pi /3 [/tex]. My problem is that I tried to do this using the convolution, but it gaves me a sum of [tex]sin[/tex] and i don't know how to progress to solve by that way, or if it is possible to do it.