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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]].
 
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==Answer==
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==Proposed Steps to get the Answer==
Can somebody finish the following computation?
+
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_{2\pi} x[n] e^{-j \frac{2\pi}{T}nk} \\
+
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>
 
+
----
not finished, I'll come back to this later.  @_@
+
==Your Turn: Share your answer!==
 
+
*Write your solution here.
-Ty
+
 
+
 
+
 
+
 
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[[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 16:41, 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} $


Your Turn: Share your answer!

  • Write your solution here.

More exercises on computing discrete-time Fourier series

Back to ECE301

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Questions/answers with a recent ECE grad

Ryne Rayburn