How can we have a good resolution over a narrow bandwidth when we include a broad range without a lot of points?

Hey,

I have to include a broad range frequency (around 50 GHz) in my codes, and I want to see the effect of that broad range on a small range frequency (about 200 MHz). There is a nonlinear effect that I include in my code, and that is the reason that a broad range is essential for me. Because I include this broad range, I need to have many points in my code (at least about 3E5) to have a reasonable resolution over the small range. I have a written function that calculates the effect on one point by using all other points. Indeed I can see that the more the resolution of the smaller range is, the more accurate my result would be. But this causes my code to run for extremely long times, which is not efficient for me because the result should be passed to another extended code. The reason is the more points are given to that written function, the longer time it takes to do the calculation for each frequency point. I am looking for a way to overcome this issue and obtain the same results in terms of accuracy by having fewer points and passing fewer points into that written function. I have already applied spline methods and then made a selection from the points and having fewer points in that way, but the result doesn't seem to have the same accuracy as the one with a large number of points. I have attached my code and the called function.

Any comments are so much appreciated!

[John D'Errico]

You tried an interpolant, but it is inadequate. You want extremely high accuracy over a small range, but you don't want to use the time to compute the amount of data you really need.

You might consider a higher order spline interpolant.