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==Questions== | ==Questions== | ||
*What is the difference between the Fourier series of a signal, and the Fourier series coefficients for a signal? | *What is the difference between the Fourier series of a signal, and the Fourier series coefficients for a signal? | ||
| − | ** | + | The Fourier series coefficients are in terms of k, and are the coefficients of each nth progression of the signal. The Fourier series is the sum of the Fourier coefficient and nth term of the signal product. |
| + | |||
| + | For example: | ||
| + | <math> | ||
| + | \begin{align} | ||
| + | x(n) &= \sum_{n=-\infty}^\infty sin(pi*n) | ||
| + | a_k = sinc(k) <-- Fourier series coefficient | ||
| + | Therefore, x(n) = sinc(0)*sin(pi*n) + sinc(1)*sin(pi*n) + ... | ||
| + | \end{align} | ||
| + | </math> | ||
| + | At least that's how I understand it now. | ||
| + | |||
| + | ~ksoong | ||
---- | ---- | ||
[[ECE301|Back to ECE301]] | [[ECE301|Back to ECE301]] | ||
Revision as of 11:34, 16 September 2010
This pages contains exercises to practice computing the Fourier series of a CT signal
Note: This is a collective study page. You are expected to participate by adding content/comment/questions/exercises etc. This is a wiki after all!
Recall the basic formulas
- Fourier series of a continuous-time signal x(t) periodic with period T
- $ x(t)=\sum_{n=-\infty}^\infty a_n e^{j \frac{2\pi}{T}nt} $
- Fourier series coefficients of a continuous-time signal x(t) periodic with period T
- $ a_n=\frac{1}{T} \int_{0}^T x(t) e^{-j \frac{2\pi}{T}nt}dt $
Case 1: For some periodic functions, the Fourier series coefficients must be obtained by integration
- Periodic square wave with period two
- Write a page with an example here.
- write a page with another example here.
Case 2: Some periodic functions (e.g. sine and cosine) can be directly expanded into a linear combination of complex exponentials
The following pages contain a periodic signal along with a computation of the Fourier series coefficients of that signal. These were contributed by your peers in ECE301. Check whether the answers are correct. Are all the steps explained clearly and logically? Do you have questions? Feel free to comment directly on the pages!
- HW4.1_Austin_Melnyk_ECE301Fall2008mboutin
- HW4.1_Adrian_Delancy_ECE301Fall2008mboutin
- HW4.1_Ananya_Panja_ECE301Fall2008mboutin
- HW4.1_Wei_Jian_Chan_ECE301Fall2008mboutin
- HW4.1_Carlos_Leon_ECE301Fall2008mboutin
- HW4.1_Ronny_Wijaya_ECE301Fall2008mboutin
- HW4-1_Steve_Anderson_ECE301Fall2008mboutin
- HW4-1_Steve_Anderson_ECE301Fall2008mboutin
- HW4.1_Max_Paganini_ECE301Fall2008mboutin
- HW4.1_Miles_Whittaker_ECE301Fall2008mboutin
- HW4.1_Scott_Erdbruegger_ECE301Fall2008mboutin
- HW4.1_Jungu_(Joe)_Choi_ECE301Fall2008mboutin
- HW4.1_I-Cheng_CHen_ECE301Fall2008mboutin
- HW4.1_Emily_Blount_ECE301Fall2008mboutin
- HW4.1_Ben_Laskowski_ECE301Fall2008mboutin
- HW4.1_Travis_Safford_ECE301Fall2008mboutin
- HW4.1_Daniel_Morris_ECE301Fall2008mboutin
- HW4.1_Nicholas_Block_ECE301Fall2008mboutin
- HW4.1_Sean_Ray_ECE301Fall2008mboutin
- See more exercise in the first question of this page
Questions
- What is the difference between the Fourier series of a signal, and the Fourier series coefficients for a signal?
The Fourier series coefficients are in terms of k, and are the coefficients of each nth progression of the signal. The Fourier series is the sum of the Fourier coefficient and nth term of the signal product.
For example: $ \begin{align} x(n) &= \sum_{n=-\infty}^\infty sin(pi*n) a_k = sinc(k) <-- Fourier series coefficient Therefore, x(n) = sinc(0)*sin(pi*n) + sinc(1)*sin(pi*n) + ... \end{align} $ At least that's how I understand it now.
~ksoong
