Homework: Sampling: A class review: Difference between revisions
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|<math>X_s(f) {\mathrm{def}}{=}\ \mathcal{F} \left \{ x_s(t) \right \} = \int_{-\infty}^{\infty} x_s(t) e^{-i 2 \pi f t} \,dt \ </math> |
|<math>X_s(f) {\mathrm{def}}{=}\ \mathcal{F} \left \{ x_s(t) \right \} = \int_{-\infty}^{\infty} x_s(t) e^{-i 2 \pi f t} \,dt \ </math> |
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|<math>= \mathcal{F} \left \{ \sum_{k=-\infty}^{\infty} x(t) \cdot e^{i 2 \pi k f_s t} \right \} \ |
|<math>= \mathcal{F} \left \{ \sum_{k=-\infty}^{\infty} x(t) \cdot e^{i 2 \pi k f_s t} \right \} \</math> |
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To make our job easier when dealing with discrete time based equations, it is helpful to have a |
<br> To make our job easier when dealing with discrete time based equations, it is helpful to have a |
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Revision as of 17:16, 22 October 2007
Sampling: A Class Review
A continuous function has an infinite amount of information stored on it - a continuous line has an infinite amount of points on it to document. So, the only way we can manipulate transforms on the computer is to quanticize them using the Fourier series.
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle = \mathcal{F} \left \{ \sum_{k=-\infty}^{\infty} x(t) \cdot e^{i 2 \pi k f_s t} \right \} \}
To make our job easier when dealing with discrete time based equations, it is helpful to have a
