In other words, you have a series of complex numbers C[0], C[1], C[2], ... , each number associated with a frequency F[0], F[1], F[2], ...
And you want to find a value C(f) for an arbitrary f.
If (I repeat, --IF-- ) the C[] array was simple (not complex) numbers, then it's easy:
1... Make sure the F[] array is in ascending order. Sort it (and re-arrange the C[] array to match) if necessary.
2... Feed the F[] array and the f term into a THRESHOLD 1D ARRAY function (ARRAY palette). This gets you the fractional index where f would lie in the F[] array.
3... Feed that fractional index and the C[] array into a INTERPOLATE 1-D ARRAY function.
4... Out comes the C value at f, assuming that f lies within the min / max of the F[] array.
---
----------- HOWEVER ----------
The INTERPOLATE ARRAY function will not work on a COMPLEX array.... Why?
The trouble is the interpolation of complex numbers is mathematically undefined. Or, more precisely, it is defined TWO ways.
Consider two points, in rectangular notation:
2 + j0
0 + j2
What is the point halfway between them?
If you add them and divide by 2, you get the answer of 1 + j1
That is reasonable.
Consider two points, in polar notation
2 /_ 0
2 /_ 90
What is the point halfway between them?
If you average the magnitudes, and average the angles, you get:
2 /_ 45
And that, too, is reasonable.
Note that the two points are the same in either notation, but THE ANSWERS ARE DIFFERENT !
1 + j1 is NOT EQUAL to 2 /_ 45 !
It all depends on what makes sense in your application. Both answers are reasonable in certain circumstances.
This is why the INTERPOLATE function refuses to work on COMPLEX arrays.
You COULD split the complex array in
to REAL and IMAGINARY parts, interpolate each, using steps 1-4 above, and combine the two results back into a complex number. Is it the RIGHT number? Only you can judge that.
