Automatic drift/offset cancellation in noisy spectrum

[kumban]

I have a noisy signal that contains 1-20 Hz spectral information. Its amplitude is  about 1 mV. This is originating from an infrared specrometer. The issue is the offset or baseline is continuously drifting at a random manner. I have to collect several spectra for averaging. But the drift associated with one set will be different from the next. Can anyone suggest a real time drift eliminating tool ?

[Henrik_Volkers]

If you already transfer your data into the frequency domain, the DC part is your first bin. How about setting it to zero?