(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find the fourier transform of the function

[tex]

x(t)=\left\{\begin{matrix}

&25 - \frac{25}{8}|t-10| &for &|t-10|<8 \\

&0 &for& |t-10|>8

\end{matrix}\right.

[/tex]

2. Relevant equations

3. The attempt at a solution

we know that

[tex]

g(t)=\left\{\begin{matrix}

&1-|t| &for &|t|<1 \\

&0 &for& |t|>1

\end{matrix}\right.\leftrightarrow X(j\omega) =\left\{\begin{matrix}

&\begin{bmatrix}

{\frac{\frac{sin(\omega)}{2}}{\frac{\omega}{2}}}

\end{bmatrix}^{2} &for &|\omega|<1 \\

&0 &for& |\omega|>1

\end{matrix}\right.

[/tex]

we can see that [tex]x(t) = 25g(\frac{1}{8} (t-10)) [/tex]

now

[tex]25g(t-10) \leftrightarrow 25 X(j \omega) e^{-j 10 \omega} [/tex]

and

[tex] 25g(1/8(t-10)) \leftrightarrow \frac{25}{8} X(j\frac{\omega}{8}) e^{-j 10 \frac{\omega}{8}}[/tex]

is this correct?

thanks in advance

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# Homework Help: Find the fourier transform

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