One cannot interpolate a complex number in the form of Real + j*imaginary.
The only way to do interpolation is on the complex representation of an amplitude + phase. But sometimes the phase is not continuous, and given in the modulo(2*pi) representation (such as the result from the "FFT" function).

Using "unwrap" function does not always manage to restore the phase to be continuous, thus interpolation in the Fourier plane is probably the only answer.

This function works on a single or 2 dimensional arrays.