| Line 7: | Line 7: | ||
---- | ---- | ||
==Answer== | ==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 &= \frac{1}{T} \sum_{ | + | 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> | ||
| − | |||
| − | |||
| − | |||
Revision as of 14:20, 14 September 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.
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} $
