Hw8: Difference between revisions

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<math> \sum_{m=-M}^m a_{m}x[(r-m)T/2]=y(r) </math>
===Make a page about interpolating FIR filters. Take care to note how many multiply/add operations.===


The number of add/multiply operations is half the limits of the sumation above. Half results from only needing to perform calculations on half the data.
An interpolting filter is when you create "in-between" samples from the original sample resulting as if you had sampled the signal at a higher rate. Interpolation only works with integers.
The are under the rth impulse function of the interpolated signal is


<math>(2M+1)(1/2)\!</math>
<math> y(t)= \sum_{r=-\infty}^\infty y(r)\delta (t- \left(\frac{\left(rt\right) }{2} \right)) </math>


Substitute
For every T seconds, the number of add/multiply operations is


<math>r/2=n =m/2\!</math>
<math>(2M+1)(1/2)\!</math>
 
in y(r) to get the result of the interpolating filter
 
<math> y(t)= \sum_{r=-\infty}^\infty y(r)\delta (t-rT/2) </math>

Latest revision as of 18:37, 15 December 2010

Make a page about interpolating FIR filters. Take care to note how many multiply/add operations.

An interpolting filter is when you create "in-between" samples from the original sample resulting as if you had sampled the signal at a higher rate. Interpolation only works with integers.

The are under the rth impulse function of the interpolated signal is

y(t)=r=y(r)δ(t((rt)2))

For every T seconds, the number of add/multiply operations is

(2M+1)(1/2)