| Line 26: | Line 26: | ||
==Theory== | ==Theory== | ||
| − | * | + | * Review of formulas used in 301 |
{| | {| | ||
| − | |||
|- | |- | ||
| align="right" style="padding-right: 1em;" | CT Fourier Transform | | align="right" style="padding-right: 1em;" | CT Fourier Transform | ||
| Line 39: | Line 38: | ||
| − | * | + | * Review of formulas used in ECE 438. Let (\omega)= 2\pi |
| + | |||
| + | {| | ||
| + | |- | ||
| + | ! style="background: none repeat scroll 0% 0% rgb(228, 188, 126); font-size: 110%;" colspan="2" | CT Fourier Transform Pairs and Properties (frequency <span class="texhtml">f</span> in hertz) [[More on CT Fourier transform|(info)]] | ||
| + | |- | ||
| + | ! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="2" | Definition CT Fourier Transform and its Inverse | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | CT Fourier Transform | ||
| + | | <math>X(f)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i2\pi ft} dt</math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Inverse DT Fourier Transform | ||
| + | | <math>\, x(t)=\mathcal{F}^{-1}(X(f))=\int_{-\infty}^{\infty}X(f)e^{i2\pi ft} df \,</math> | ||
| + | |} | ||
| + | |||
*Thi sis a [[Main_Page| link to a Rhea page]] | *Thi sis a [[Main_Page| link to a Rhea page]] | ||
==Example== | ==Example== | ||
Revision as of 09:10, 18 September 2014
Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f
A slecture by ECE student JOE BLO
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
OUTLINE
- Introduction
- Theory
- Examples
- Conclusion
- References
Introduction
In my slecture I will explain Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f (in hertz).
Theory
- Review of formulas used in 301
| CT Fourier Transform | $ \mathcal{X}(\omega)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i\omega t} dt $ |
| Inverse DT Fourier Transform | $ \, x(t)=\mathcal{F}^{-1}(\mathcal{X}(\omega))=\frac{1}{2\pi} \int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{i\omega t} d \omega\, $ |
- Review of formulas used in ECE 438. Let (\omega)= 2\pi
| CT Fourier Transform Pairs and Properties (frequency f in hertz) (info) | |
|---|---|
| Definition CT Fourier Transform and its Inverse | |
| CT Fourier Transform | $ X(f)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i2\pi ft} dt $ |
| Inverse DT Fourier Transform | $ \, x(t)=\mathcal{F}^{-1}(X(f))=\int_{-\infty}^{\infty}X(f)e^{i2\pi ft} df \, $ |
- Thi sis a link to a Rhea page
Example
- THIS IS THE FIRST ITEM
- THIS IS THE SECONF ITEM
Post your slecture material here. Guidelines:
- If you wish to post your slecture anonymously, please contact your instructor to get an anonymous login. Otherwise, you will be identifiable through your Purdue CAREER account, and thus you will NOT be anonymous.
- Rephrase the material in your own way, in your own words, based on Prof. Boutin's lecture material.
- Feel free to add your own examples or your own material.
- Focus on the clarity of your explanation. It must be clear, easily understandable.
- Type text using wikitext markup language. Do not post a pdf. Do not upload a word file.
- Type all equations using latex code between <math> </math> tags.
- You may include graphs, pictures, animated graphics, etc.
- You may include links to other Project Rhea pages.
IMPORTANT: DO NOT PLAGIARIZE. If you use other material than Prof. Boutin's lecture material, you must cite your sources. Do not copy text word for word from another source; rephrase everything using your own words. Similarly for graphs, illustrations, pictures, etc. Make your own! Do not copy them from other sources.
(create a question page and put a link below)
Questions and comments
If you have any questions, comments, etc. please post them on this page.
