6.27.30  Trigonometric interpolation: triginterp

The triginterp command computes a trigonometric polynomial which interpolates given data.

• triginterp takes four arguments:
  • L, a list of numbers.
  • a, a number (the beginning of an interval).
  • b, a number (the end of the interval).
  • x, the name of a variable.
  The last three arguments can also be given as x=a..b.
• triginterp(L,a,b,x) or triginterp(L,x=a..b) returns the trigonometric polynomial that interpolates data given in the list L. It is assumed that the list L contains ordinate components of the points with equidistant abscissa components between a and b such that the first element of L corresponds to a and the last element to b.

Example.
For example, y may be a list of experimental measurements of some quantity taken in regular intervals, with the first observation at time t=a and the last observation at time t=b. The resulting trigonometric polynomial has period

where n is the number of observations (n=size(y)). As a specific example, assume that the following data is obtained by measuring the temperature every three hours:

Furthermore, assume that an estimate of the temperature at 13:45 is required. To obtain a trigonometric interpolation of the data:
Input:

Output:

Now a temperature at 13:45 hrs can be approximated with the value of tp for x=13.75.
Input:

Output:

If one of the input parameters is inexact, the result will be inexact too. For example:
Input:

Output: