Line 11: Line 11:
  
 
and <math> \frac {x(t_{k+1})-x(t_k)}{t_{k+1} - t_k} </math> is just the slope.
 
and <math> \frac {x(t_{k+1})-x(t_k)}{t_{k+1} - t_k} </math> is just the slope.
 +
 +
And as you can see the smaller the sampling is the better chance you have of what the signal looks like.

Revision as of 16:14, 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.

And as you can see the smaller the sampling is the better chance you have of what the signal looks like.

Alumni Liaison

BSEE 2004, current Ph.D. student researching signal and image processing.

Landis Huffman