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<math> x(t) = \sum^{\infty}_{k = -\infty} x(kT) (u[t-kT]-u[t-(k+1)T])</math> | <math> x(t) = \sum^{\infty}_{k = -\infty} x(kT) (u[t-kT]-u[t-(k+1)T])</math> | ||
| − | 2. To step it up we can use 1st order interpolation. She gave an example about a kid going to an interview and they asked him if he has ever heard | + | 2. To step it up we can use 1st order interpolation. She gave an example about a kid going to an interview and they asked him if he has ever heard of splines and peace-wise polynomial functions and that is what this is. |
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| + | <math>x(t)= \sum^{\infty}_{k = -\infty} x(t_k) + (t-t_k \frac {x(t_{k+1})-x(t_k)}{t_{k+1} - t_k}) </math> | ||
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| + | and <math> \frac {x(t_{k+1})-x(t_k)}{t_{k+1} - t_k} </math> is just the slope. | ||
Revision as of 15:11, 10 November 2008
Can we ever reconstruct a a signal by its sampling? No, we generally never can but we can approximate.
1. The easiest way to "reconstruct" a signal is by zero-order interpolation which looks like step functions.
$ x(t) = \sum^{\infty}_{k = -\infty} x(kT) (u[t-kT]-u[t-(k+1)T]) $
2. To step it up we can use 1st order interpolation. She gave an example about a kid going to an interview and they asked him if he has ever heard of splines and peace-wise polynomial functions and that is what this is.
$ x(t)= \sum^{\infty}_{k = -\infty} x(t_k) + (t-t_k \frac {x(t_{k+1})-x(t_k)}{t_{k+1} - t_k}) $
and $ \frac {x(t_{k+1})-x(t_k)}{t_{k+1} - t_k} $ is just the slope.
