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| − | =Exercise: Compute the Fourier series coefficients of the following signal | + | =Exercise: Compute the Fourier series coefficients of the following signal:= |
<math>x(t)=\left\{\begin{array}{ll}1&\text{ when } 0\leq t <1 \\ 0& \text{ when } 1\leq t <2\end{array} \right.</math> | <math>x(t)=\left\{\begin{array}{ll}1&\text{ when } 0\leq t <1 \\ 0& \text{ when } 1\leq t <2\end{array} \right.</math> | ||
| − | x(t) periodic with period two. | + | x(t) periodic with period two. |
| + | |||
| + | After you have obtained the coefficients, write the Fourier series of x(t). | ||
---- | ---- | ||
==Answer== | ==Answer== | ||
| − | + | Can somebody finish the following computation? | |
| − | + | ||
| + | <math> | ||
| + | \begin{align} | ||
| + | a_n &= \frac{1}{T} \int_{0}^T x(t) e^{-j \frac{2\pi}{T}nt}dt \\ | ||
| + | & =\frac{1}{2} \int_{0}^2 x(t) e^{-j \frac{2\pi}{2}nt}dt \\ | ||
| + | & = | ||
| + | \end{align} | ||
| + | </math> | ||
---- | ---- | ||
| + | [[Recommended_exercise_Fourier_series_computation|More exercises on computing continuous-time Fourier series]] | ||
| + | |||
[[ECE301|Back to ECE301]] | [[ECE301|Back to ECE301]] | ||
Revision as of 07:54, 14 September 2010
Exercise: Compute the Fourier series coefficients of the following signal:
$ x(t)=\left\{\begin{array}{ll}1&\text{ when } 0\leq t <1 \\ 0& \text{ when } 1\leq t <2\end{array} \right. $
x(t) periodic with period two.
After you have obtained the coefficients, write the Fourier series of x(t).
Answer
Can somebody finish the following computation?
$ \begin{align} a_n &= \frac{1}{T} \int_{0}^T x(t) e^{-j \frac{2\pi}{T}nt}dt \\ & =\frac{1}{2} \int_{0}^2 x(t) e^{-j \frac{2\pi}{2}nt}dt \\ & = \end{align} $
