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ece205: complete course!

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eggy 2023-11-28 13:34:03 -05:00
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@ -542,6 +542,10 @@ $$\int^\infty_{-\infty}[f(t)]^2dt=\frac{1}{2\pi}\int^\infty_{-\infty}|\hat f(\om
- FT/IFT are linear: $\mathcal F\{af+bg\}=a\mathcal F\{f\}+b\mathcal F\{g\}$ - FT/IFT are linear: $\mathcal F\{af+bg\}=a\mathcal F\{f\}+b\mathcal F\{g\}$
- FT is scalable: $\mathcal F\{f(ax)\}=\frac 1 a\hat f\left(\frac{\omega}{a}\right)$ - FT is scalable: $\mathcal F\{f(ax)\}=\frac 1 a\hat f\left(\frac{\omega}{a}\right)$
- FT can shift frequencies: $\mathcal F\{e^{iax}f(x)\}=\hat f(\omega-a)$
- FT can shift time: $\mathcal F\{f(x-a)\}=e^{ia\omega}\hat f(\omega)$
- If the IFT is applicable: $\mathcal F\{f^{(n)}(x)\}=(i\omega)^n\hat f(\omega)$
- The FT is symmetrical: $\mathcal F\{\hat f(x)\}=2\pi f(-\omega)$
## Resources ## Resources