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* First let's review formulas we used in 301 | * First let's review formulas we used in 301 | ||
| − | + | {| | |
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| + | ! 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">ω</span> in radians per time unit) [[More on CT Fourier transform|(info)]] | ||
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| + | ! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="2" | Definition CT Fourier Transform and its Inverse | ||
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| align="right" style="padding-right: 1em;" | [[More on CT Fourier transform|(info)]] CT Fourier Transform | | align="right" style="padding-right: 1em;" | [[More on CT Fourier transform|(info)]] CT Fourier Transform | ||
| <math>\mathcal{X}(\omega)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i\omega t} dt</math> | | <math>\mathcal{X}(\omega)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i\omega t} dt</math> | ||
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| align="right" style="padding-right: 1em;" | [[More on CT Fourier transform|(info)]] Inverse DT Fourier Transform | | align="right" style="padding-right: 1em;" | [[More on CT Fourier transform|(info)]] Inverse DT Fourier Transform | ||
| <math>\, x(t)=\mathcal{F}^{-1}(\mathcal{X}(\omega))=\frac{1}{2\pi} \int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{i\omega t} d \omega\,</math> | | <math>\, x(t)=\mathcal{F}^{-1}(\mathcal{X}(\omega))=\frac{1}{2\pi} \int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{i\omega t} d \omega\,</math> | ||
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*This is the second bullet | *This is the second bullet | ||
*Thi sis a [[Main_Page| link to a Rhea page]] | *Thi sis a [[Main_Page| link to a Rhea page]] | ||
Revision as of 08:56, 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.
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
- First let's review formulas we used in 301
| CT Fourier Transform Pairs and Properties (frequency ω in radians per time unit) (info) | |
|---|---|
| Definition CT Fourier Transform and its Inverse | |
| (info) CT Fourier Transform | $ \mathcal{X}(\omega)=\mathcal{F}(x(t))=\int_{-\infty}^{\infty} x(t) e^{-i\omega t} dt $ |
| (info) 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\, $ |
- This is the second bullet
- 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.
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Questions and comments
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