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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 09:56, 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:
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- Rephrase the material in your own way, in your own words, based on Prof. Boutin's lecture material.
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Questions and comments
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