I can't speak to any of the high-level mathematics, but it seems that you could do a reverse FFT transform on the data, convert it to a waveform, and spectrum analyze it in LabVIEW. I'm assuming that by "spectrum analyzing" it you mean that you want to display the signal on an amplitude vs. frequency graph. Below I've listed the necessary VIs to implement the process I described above:
Inverse FFT: All Functions»Analyze»Signal Processing»Frequency Domain
Build Waveform: All Functions»Waveform
FFT Power Spectrum: All Functions»Analyze»Waveform Measurements
That last function will return a waveform in the amplitude/frequency domain, which you can then route directly to a graph. Hope this helps!
Regards,
E. Sulzer
Applications Engineer
National Instruments