Interpolation of measured data

• Nov 10th 2005, 12:46 PM
jhasting
Interpolation of measured data
I have a measured data set (x & y are inputs, z is the result at those measures):

x y z
0.036802 0.004908 0.07158
0.036802 0.022135 0.10095
0.130886 0.004908 0.09627
0.130886 0.022135 0.12560

I would like a formula for interpolation, to predict z for all input conditions x & y (within bounds), for example when x=0.0875 & y=0.0066.

I have tried some some formulas, but nothing is predicting with much accuracy.

Thanks for any help
J
• Nov 10th 2005, 11:08 PM
CaptainBlack
Interpolation of measured data
Quote:

Originally Posted by jhasting
I have a measured data set (x & y are inputs, z is the result at those measures):

x y z
0.036802 0.004908 0.07158
0.036802 0.022135 0.10095
0.130886 0.004908 0.09627
0.130886 0.022135 0.12560

I would like a formula for interpolation, to predict z for all input conditions x & y (within bounds), for example when x=0.0875 & y=0.0066.

I have tried some some formulas, but nothing is predicting with much accuracy.

Thanks for any help
J

As always with problems of this type it would be helpfull to
know what process gives rise to the data, then we could fit
it with to an appropriate function.

However lacking such knowlege you could always try the
4-point interpolator given in Abramowitz and Stegun:

Suppose you know your functional value at points:

$\displaystyle (x_0,y_0),\ (x_0+h,y_0),\ (x_0,y_0+k),\ (x_0+h,y_0+k)$

then

$\displaystyle f(x_0+p.h,y_0+q.k)\ \approx \ (1-p).(1-q).f(x_0,y_0)\ +$
$\displaystyle p.(1-q).f(x_0+h,y_0)\ +$

$\displaystyle (1-p).q.f(x_0,y_0+k)\ +$

$\displaystyle p.q.f(x_0+h,y_0+k)$
Preferably with $\displaystyle 0 \leq p \leq 1$ and $\displaystyle 0 \leq q \leq 1$.
• Nov 11th 2005, 06:43 AM
jhasting
Thanks, I don;t think your formula will work in this case. This data is measured data, it does not have a fucntion. The application is for CMOS ASIC circuit design static timing. Libraries are modeled at certain operating conditions and specified in tables. THe x axis data I provided would be the input transition of the wire to a logic gate pin, the y asix data I provided would be the output capatance of the wire to the logic gate output pin. Since fast results are required, interpolaion of the data is used. So for a logic cell modeled in a library, if you know the input transition and the output capactance, you should be able to interpolate the delay. The only requirement on the data should be that the input transition (x axis data) is within it's bounds, and hte same with the output capactance y data. I cannot use equations with more restrictions.

Thanks for any help, and any time you've already spent.
J
• Nov 11th 2005, 09:48 AM
CaptainBlack
Quote:

Originally Posted by jhasting
Thanks, I don;t think your formula will work in this case. This data is measured data, it does not have a fucntion. The application is for CMOS ASIC circuit design static timing. Libraries are modeled at certain operating conditions and specified in tables. THe x axis data I provided would be the input transition of the wire to a logic gate pin, the y asix data I provided would be the output capatance of the wire to the logic gate output pin. Since fast results are required, interpolaion of the data is used. So for a logic cell modeled in a library, if you know the input transition and the output capactance, you should be able to interpolate the delay. The only requirement on the data should be that the input transition (x axis data) is within it's bounds, and hte same with the output capactance y data. I cannot use equations with more restrictions.

Thanks for any help, and any time you've already spent.
J

Just use you measured values for the f values in the formula,
it will do the interpolation for you

RonL
• Nov 11th 2005, 09:53 AM
jhasting
The tables do not have all values for trans & cap, they are usually 7x7, so you need to interpolate.
• Nov 11th 2005, 10:23 AM
CaptainBlack
Quote:

Originally Posted by jhasting
The tables do not have all values for trans & cap, they are usually 7x7, so you need to interpolate.

I give up. What I have quoted is an interpolation formula
which allows you to interpolate into data tabulated on a
regular grid.

RonL