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=Exercise: Compute the DT Fourier series coefficients of the following discrete-time signal:= | =Exercise: Compute the DT Fourier series coefficients of the following discrete-time signal:= | ||
| − | <math>x | + | <math>x[n]=\sum_{k=-\infty}^\infty \left( u[n-5k]-u[n-4-5k] \right) </math> |
| − | After you have obtained the coefficients, write the Fourier series of x | + | After you have obtained the coefficients, write the Fourier series of x[n]. |
Help: If the function above does not look periodic to you, please read [[Hw1periodicECE301f08profcomments|this page]]. | Help: If the function above does not look periodic to you, please read [[Hw1periodicECE301f08profcomments|this page]]. | ||
---- | ---- | ||
| − | ==Answer== | + | ==Proposed Steps to get the Answer== |
| − | + | The first step is to figure out the period N of x[n]. | |
| + | |||
| + | .....please fill in.... | ||
| + | |||
| + | |||
| + | Then, one needs to find the coefficients using the summation formula | ||
| + | |||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
| − | a_n &= \ | + | a_n &= \frac{1}{T} \sum_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk}, \text{ by the definition of Fourier series coefficients,} \\ |
| − | & = ... | + | & = ...\\ |
| + | & = ... \text{ please finish } | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
| − | + | ---- | |
| − | + | ==Your Turn: Share your answer!== | |
| − | + | *Write your solution here. | |
---- | ---- | ||
[[Recommended_exercise_Fourier_series_computation_DT|More exercises on computing discrete-time Fourier series]] | [[Recommended_exercise_Fourier_series_computation_DT|More exercises on computing discrete-time Fourier series]] | ||
[[ECE301|Back to ECE301]] | [[ECE301|Back to ECE301]] | ||
Latest revision as of 15:41, 30 November 2010
Exercise: Compute the DT Fourier series coefficients of the following discrete-time signal:
$ x[n]=\sum_{k=-\infty}^\infty \left( u[n-5k]-u[n-4-5k] \right) $
After you have obtained the coefficients, write the Fourier series of x[n].
Help: If the function above does not look periodic to you, please read this page.
Proposed Steps to get the Answer
The first step is to figure out the period N of x[n].
.....please fill in....
Then, one needs to find the coefficients using the summation formula
$ \begin{align} a_n &= \frac{1}{T} \sum_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk}, \text{ by the definition of Fourier series coefficients,} \\ & = ...\\ & = ... \text{ please finish } \end{align} $
- Write your solution here.
