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## Homework Statement

Find the Fourier spectrum ##C_k## of the following function and draw it's graph:

## Homework Equations

3. The Attempt at a Solution [/B]

I know that the complex Fourier coefficient of a rectangular impulse ##U## on an interval ##[-\frac{\tau}{2}, \frac{\tau}{2}]## is ##C_k = \frac{U\tau}{T}\frac{\sin {kw\frac{\tau}{2}}}{kw\frac{\tau}{2}}## and since ##f(t)=U\cos {w_ot}## i can say that ##f(t)=\frac{U}{2}(e^{jw_ot}-e^{-jw_ot})## which if i use the property of the Fourier series get:

##C_k = \frac{U\tau}{T}\frac{\sin {k(w+w_o)\frac{\tau}{2}}}{k(w+w_o)\frac{\tau}{2}} - \frac{U\tau}{T}\frac{\sin {k(w-w_o)\frac{\tau}{2}}}{k(w-w_o)\frac{\tau}{2}}##. Is this correct. How would i draw a graph of this?