How to resize the array of complex values with interpolation method in python?

I am not sure if I understood correctly but I think that treating separately real and imaginary part of the numbers should be sufficient.

I understand that there is an array of complex numbers

(x_1+i*y_1),(x_2+i*y_2),(x_3+i*y_3),...,(x_n+i*y_n)

You cannot interpolate an array. Interpolation is usually related to approximating an unknown function i.e.

finding a polynomial that contains certain points (x_1,y_1), (x_2,y_2), .... , (x_n,y_n) where we assume

(we usually obtain these values by measurement)

that f(x_i)=y_i. There are several interpolation polynomials that you can use depending on the nature of your data.

The main problem here is what are x_i and what is y_i in this case. There are several possibility and none of them guaranties good results.

The reason for that lies in the fact that you can "fill" gaps in your array in arbitrarily number of ways.

Some, possibly helpful, ideas:

1. Create interpolation polynomial using pairs (x_1,y_1), (x_2,y_2), .... , (x_n,y_n)

lets say that you obtain a certain polynomial L. With L you have a certain relationship between real and imaginary part

of complex numbers. After that choose a real part a_1 and calculate the corresponding imaginary part of the complex number.

Precisely calculate L(a_1) and name it b_1. So now you have a complex

number a_1+i*b_1. Repeat the procedure.

2. If there is an underlying "originals" (for example time when you obtain the samples you could use that as well.

For example in t_n you get a complex number x_n+i*y_n. So determine an interpolation polynomial L_1 for real parts

(t_1,x_1),...,(t_n,x_n) and another polynomial L_2 for imaginary parts. So choose a time t and calculate real part L_1(t)

(denoted by A) and imaginary part L_2(t) (denoted by B). So you get the complex number, A+i*B. Repeat the procedure.

If there is no such underlying "originals", you could assume t_1=1,t_2=2, ... and see if it suits you.

However, as I said there is no guaranties that you achieve what you want because "between x_1+i*y_1 and x_2+i*y_2"

any complex number could fit depending on the "true nature of your problem".

I hope that this was of some help.