triginterp(y,x=a..b) or triginterp(y,a,b,x) returns the trigonometric polynomial that interpolates data given in the list y . It is assumed that the list y contains ordinate components of the points with equidistant abscissa components between a and b such that the first element from y corresponds to a and the last element to b .
For example, y may be a list of experimental measurements of some quantity taken in regular intervals, with the first observation in the moment t=a and the last observation in the moment t=b . The resulting trigonometric polynomial has the period
where n is the number of observations ( n =size(y)). For example, assume that the following data is obtained by measuring the temperature every three hours:
|hour of the day||0||3||6||9||12||15||18||21|
|temperature (deg C)||11||10||17||24||32||26||23||19|
Furthermore, assume that an estimate of the temperature at 13:45 is required. To obtain a trigonometric interpolation of the data, input :
Now a temperature at 13:45 hrs can be approximated with the value of tp for x=13.75 . Input :
If one of the input parameters is inexact, the result will be inexact too. For example, input :