Hw8: Difference between revisions

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


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


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


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


<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 17:37, 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

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