Can a bipolar EEG signal be converted to a monopolar (unipolar) one? I have bipolar EEG signal of Fpz-Cz of EEG sleep data which I have downloaded from physionet. I would like to have Fpz signal for my sleep study.

Is there any way I could convert a bipolar EEG signal to a monopolar (unipolar) EEG signal?
Short answer
As far as I can see - no you can't. 

Background
In EEG systems, unipolar signals are measurements against a distant reference electrode, for example Fpz (Fig. 1). So suppose I have recorded unipolar EEG signals, say O1 and O2 against Fps, then I can obtain a bipolar measurement offline by subtracting O1-O2 (source: Biopac). 

However, if you start with a bipolar measurement, e.g. O1-O2, then you can never reduce those recordings back to O1-Fpz and O2-Fpz as the O1 and O2 signals are independent of Fpz.

Further, 'the' Fpz signal is non-existant, as an electrophysiological potential (and in fact any potential), is a potential difference between 2 points. There is no potential difference on one electrode.        

PS. 
I am not proficient in principal component analysis, but I do know that by cross-correlating various electrode-pairs a source analysis can be done. Perhaps you could somehow extract the unipolar signal from bipolar signals, but I must say that a Google Scholar search using the search terms 'principal + component + analysis + eeg + bipolar + to + unipolar' did not yield any useful hits, at least at first glance. 


Fig.1. EEG montage. source: Kemp et al., 2003