Richard Owlett
04-12-2008, 02:33 PM
I'm working on a "problem" that got me thinking.
As the purpose of attempting the "problem" was education that's good.
I have 96 data points.
I desire:
1. approximation of 97th (but NOT 98th or greater).
2. interpolate 28 intervening data points, including between points
96 and 97.
I know a priori that:
1. the function and ALL derivatives are continuous.
2. the function is almost periodic.
a. 1 period ends ~3/4 ow way between points 96 and 97.
b. The deviations from periodic behavior are small and in
themselves periodic but with periods 30 to 300 times longer
than my total sample time.
Scilab's smooth() function appears to handle the interpolations from
points 1 thru 96.
Can DSP techniques or point of view:
1. get me a better interpolation?
2. get me point 97?
[ The 96 data points are satellite positions in an Earth Centered Earth
Fixed (ECEF) frame of reference from Rinex formated data files running
nominally from midnight to midnight. Unfortunately, the closing
"midnight" is in the next day's data file (which will not always be
accessible). As orbits are well defined, I could convert from ECEF to
inertial frames, interpolate and extrapolate, and convert back to ECEF.
That has it's own set of *MASSIVE* problems for me.]
Comments?
As the purpose of attempting the "problem" was education that's good.
I have 96 data points.
I desire:
1. approximation of 97th (but NOT 98th or greater).
2. interpolate 28 intervening data points, including between points
96 and 97.
I know a priori that:
1. the function and ALL derivatives are continuous.
2. the function is almost periodic.
a. 1 period ends ~3/4 ow way between points 96 and 97.
b. The deviations from periodic behavior are small and in
themselves periodic but with periods 30 to 300 times longer
than my total sample time.
Scilab's smooth() function appears to handle the interpolations from
points 1 thru 96.
Can DSP techniques or point of view:
1. get me a better interpolation?
2. get me point 97?
[ The 96 data points are satellite positions in an Earth Centered Earth
Fixed (ECEF) frame of reference from Rinex formated data files running
nominally from midnight to midnight. Unfortunately, the closing
"midnight" is in the next day's data file (which will not always be
accessible). As orbits are well defined, I could convert from ECEF to
inertial frames, interpolate and extrapolate, and convert back to ECEF.
That has it's own set of *MASSIVE* problems for me.]
Comments?