One approach is to first, negate the frequencies. And then offset them so they are all greater than 0 again.
Imagine you had a simple spectrum with frequencies (100 200 300 400). When you negate the frequencies you get (-100 -200 -300 -400). Now, if you add an offset of 500, you will get: (400 300 200 100). Since you have changed the order of the frequencies but have not changed the amplitudes, the effect is an inverted spectrum.
For most live spectra, the effect will be to have very bright timbres, where the high partials are weighted more heavily than the low partials.
In the Kyma Sound Library, if you search by Sound name for Invert Spectrum of Live Input, you'll find an example.
Let us know how it goes!