Due: end of semester
Because of his newly found confidence in your ability, Biro Kratt has just assigned you to a more challenging project. It appears that the ACME Super Power Usefully Transmitting Nice Information Komputer satellite has begun to malfunction. Your boss swears that it's the last piece of high-tech equipment he will ever buy at a rummage sale. However, the malfunction may still be dealt with, and you have been assigned the task of overcoming the difficulty.
The nature of the malfunction is that 80% of the signal is getting lost in static. Your job is to try to reconstruct the signal based on the 20% of the signal that is getting through. You will attempt to do this using interpolation. In the table below, a part of SPUTNIK's signal has been transcribed. Write a program which reads in this information, and produces a table of signal values spaced at 0.1 second intervals. Use cubic splines to solve this problem.
| TIME | SIGNAL |
| 0.0 | 1.0 |
| 0.5 | 2.995 |
| 1.0 | 3.9801 |
| 1.5 | 4.9553 |
| 2.0 | 5.9211 |
| 2.5 | 6.8776 |
| 3.0 | 7.8253 |
| 3.5 | 8.7648 |
| 4.0 | 9.6967 |
| 4.5 | 10.6216 |
| 5.0 | 11.5303 |
You should hand in a listing, email me your program, and hand in a table of values from 0 to 5 spaced in .1 second intervals. Explain, in writing, to your boss, how your program works.
Extra credit, compare these results with what you would get with Lagrange interpolation. (An additional program)