Addicted to LaTex (AMA) Watch

Resonance234
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Last edited by Resonance234; 4 weeks ago
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keptinside
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What is the radius of your head?
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Notnek
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(Original post by Resonance234)
Hi

I spend a lot of my free time typing equations and solving math on the computer using LaTex.

I had dyslexia in high school but now its mostly gone.

Could it be LaTex cured me of it? We seriously need to investigate teaching math through LaTex.

 f(t) = \dfrac{a_{0}}{2} + \displaystyle \sum_{k = 1}^{k \to \infty} \bigg( | A_{k} | \cos( k \omega_{0} t - \phi_{(ab)} ) \bigg)
Can you make a nice picture using \LaTeX?
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Resonance234
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(Original post by Notnek)
Can you make a nice picture using \LaTeX?
                               
Last edited by Resonance234; 4 weeks ago
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Resonance234
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...

\textbf{Fourier transform of a dirac pulse train} 



f(t) = \text{III}_{T_{s}}(t) = \displaystyle \sum_{k \to - \infty}^{k \to \infty} \delta(t - k T_{s} )

It is equal to:


X(j \omega) = \omega_{s} \text{III}_{\omega_{s}}(t)

And the proof relies on:
1. The theorem on the fourier transform a peridioc signal.
2. The duality theorem and its application with regard to complex exponentials having the dirac pulse as its pair.


Now:


f(t)  = \displaystyle \sum_{k \to - \infty}^{k \to \infty} c_{k} e^{j (k \omega_{0} t) }
Taking the fourier transform on both sides:


\mathcal F{ f(t) } = \mathcal F {\displaystyle \sum_{k \to - \infty}^{k \to \infty} c_{k} e^{j (k \omega_{0} t) } }


\mathcal F {\displaystyle \sum_{k \to - \infty}^{k \to \infty} c_{k} e^{j (k \omega_{0} t) } } = c_{k} \cdot 2 \pi \cdot \displaystyle \sum_{k \to - \infty}^{k \to \infty}\delta(\omega - k \omega_{s})
Finding the complex fourier series co efficients c k:



c_{k} = \dfrac{1}{T_{s}} \cdot \displaystyle \int_{0}^{T_{s}} f(t) \,\,\,\, \text{d}t = \dfrac{1}{T_{s}} \cdot \displaystyle \int_{0}^{T_{s}}  \delta(t -  T_{s} )  \,\,\,\, \text{d}t = \dfrac{1}{T_{s}} = c_{k}
Now:


\dfrac{1}{T_{s}}  \cdot 2 \pi \cdot \displaystyle \sum_{k \to - \infty}^{k \to \infty}\delta(\omega - k \omega_{s})



\mathcal F \bigg[\text{III}_{T_{s}}(t) \bigg] =  \omega_{s} \cdot \displaystyle \sum_{k \to - \infty}^{k \to \infty}\delta(\omega - k \omega_{s}) \blacksquare
Last edited by Resonance234; 4 weeks ago
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angelike1
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i thought you mean latex like latex gloves and was like wtf??
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Resonance234
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(Original post by angelike1)
i thought you mean latex like latex gloves and was like wtf??
i know, its supposedly pronounced LaTECH and that was my initial reaction when I learned about it.
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Resonance234
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Is this correct?
 

\displaystyle \sum_{k =1 }^{k \to \infty} z^{n} = \dfrac{1}{1 - z} \,\,\,\,\,\,\, \text{i.f.f} |z| < 1

 

\displaystyle \sum_{k =1 }^{k = n} z^{n} = \dfrac{1}{1 - z^{n + 1 } } \,\,\,\,\,\,\, \text{i.f.f} |z| < 1
Last edited by Resonance234; 4 weeks ago
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NotNotBatman
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(Original post by Resonance234)
Is this correct?
 

\displaystyle \sum_{k =1 }^{k \to \infty} z^{n} = \dfrac{1}{1 - z} \,\,\,\,\,\,\, \text{i.f.f} |z| < 1

 

\displaystyle \sum_{k =1 }^{k = n} z^{n} = \dfrac{1}{1 - z^{n + 1 } } \,\,\,\,\,\,\, \text{i.f.f} |z| < 1
k isn't even in the sum, so no.
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Sinnoh
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 \begin{matrix} T & h & i & s & . & . & . & . & .  \\ i & s &.  & . & . & . & . & . & . \\ s & o &.  & . & . & . & . & . & . \\ s & a & d  & . & . & . & . & . & . \\ A & l & e  & x & a & . & . & . & . \\ p & l & a  & y & . & . & . & . & . \\ D & e & s & p & a & c & i & t & o \\  \end{matrix}
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NotNotBatman
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(Original post by Sinnoh)
 \begin{matrix} T & h & i & s & . & . & . & . & .  \\ i & s &.  & . & . & . & . & . & . \\ s & o &.  & . & . & . & . & . & . \\ s & a & d  & . & . & . & . & . & . \\ A & l & e  & x & a & . & . & . & . \\ p & l & a  & y & . & . & . & . & . \\ D & e & s & p & a & c & i & t & o \\  \end{matrix}
Hey, the third column spells ideas, hmm.
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