Highly interpolate complex spectrum

Good afternoon,

I have a complex spectrum of a signal that is centered around a center frequency with a certain bandwidth. I can find the center frequency by weighting each frequency bin according to the magnitude. But, the frequency resolution is not good enough for my application. Therefore the resulting center frequency of the spectrum is not accurate enough. The frequency resolution should be better by a factor of 10k. Interpolating the signal with a FFT fails because of memory issues. Anyone with a solution?

Thank you