To the extent of my knowledge the usable portion of the EEG is from 0-40 Hz which contains all the four rhythms. This excludes the 50 Hz frequency which is the noise.In this case you can use a low pass filter with the appropriate cut off frequency to keep only the data from the 0-40 Hz frequency range and discard the rest.

If this is not the case and you require data on a range including the  %0 Hz e.g. on a range from 0-100 Hz then you can design a notch filter (a filter which stops a particular frequency) of 50 Hz to stop only the noise frequency and let the others pass.

Implementations of both the schemes are possible in both hardware and software but I would recommend a software implementation using software like eeglab etc.

The most of the software's allow to set a display (also notch) filter for a certain frequency (user defined). This helps because raw data is being recorded while in the screen you see the data filtered. Then, offline, you can filter the data as you wish.

Muhammad and Joao are right for your case, where you have to obviously record EEG from patients, where it is not possible to shield the subject from AC. Here you have to find a compromise. For experiments with non-patient subjects it is absolutely possible to shield them from AC influences with a Faraday cage (at least to a very great extend). With respect to data quality, this would be the best option.

On the other hand, as explained, you can use a notch filter around 50Hz. But before you apply any filter techniques, ask yourself if this is necessary. If you are not interested in data above 40Hz, as Muhammad explained, a notch filter would not be necessary. You have to be very cautios with the use of filters, because they can probably distort your results, depending on your dependent variables (e.g. ERPs) and your research question (e.g. timing of components).

thank you all for your input. I do already use digital low-pass and notch filters, but this does not filter the 50 Hz from the actual recording, resulting in noisy ERPs. I guess I could ask for an analog filter, if it is possible to adapt it to the existing amplifiers (Mitsar). Unfortunately, the problem arises at the Intensive Care Unit (ICU), where I have no cotrol over the electrical noise. My original idea (and question) is whether I can construct some portable Faraday insulation for the amplifier box as well as for all cables and wires.

I think shielding is done in all sorts of applications ranging from computer electronics to large scale electrical instruments. I would suggest that you modify the question and mention that you require to design shields to prevent electromagnetic interference and that include EMI/EMC as the topics in which this question is posted to draw views from that community as well.

If you are having issues with distortion it is probably an issue in the filter design. I think you should use the filter design toolbox in matlab to first visualize the filter before application.

Analog filter is also a good option. 

Ground loops are another possible source of persistent 50Hz interference. Normally, depending on the system you use, there is an "isolated ground" electrode in the cap that is connected to amplifier zero volts but is electrically isolated from mains ground for safety reasons. The participant should not therefore be connected to another ground - this is hazardous as well as a potential source of 50Hz. This situation might arise inadvertently if the participant is connected to any other equipment or is in contact directly or indirectly with an equipment casing - or with a Faraday Cage! Ground loops can also arise when the ground point of different items of apparatus is different. To avoid ground loops all equipment (but not the participant) should be connected to the same ground point.  If you are using the ground of the mains supply, this needs to be a good ground. It is necessary for those responsible for electrical safety to go round with a multimeter to check the integrity of paths to ground of apparatus and of the mains supply. A possible reference source on tracking down and eliminating noise is Cutmore & James,  International Journal of Psychophysiology 32 1999 129-150

Sometimes the 50Hz noise could be entering to your register via the non-used EEG channels. Be sure that all the channels of your equipment are attached to an electrode or grounded. This non-used channels could form antennas and in an environment like ICU there's a lot of 50Hz noise. The use of an analog filter is always an option, but attach it to your equipment surely will be a headache. And the use of a Faraday cage seems like catch flies with muskets. Before thinking in an extreme solution double or triple check your acquisition setup, probably a lose wire is causing the contamination. Any or all of the above ideas will work.

"I do already use digital low-pass and notch filters, but this does not filter the 50 Hz from the actual recording"

That sounds odd. Are you sure that your filters work properly? I would check them first before investing in expensive hardware (such as a Faraday cage). Further, if you use a good low-pass filter (e.g. 40 or 45 Hz) , there is no need for an additional notch filter - it would just use up system resources and introduce potential sources of error.

The use of analog filters mainly makes sense for anti-aliasing purposes during data acquisition, unless you have to analyze data in real-time (I assume you don't, as you mentioned ERPs). Usually it is better to process data offline with digital filters, because you can't unfilter filtered data. 

cheers,

Tobi

Efthymios, you say that you are using a Mitsar amp. Can you try possibly testing with another manufacturer's amp? Some amps inject a 180 degree out of phase common mode noise signal on the Neutral (Ground / Bias) leads. This helps to cancel out the majority of mains noise. The Texas Instruments ADS1299 does this particularly well (see 2nd link). It's hard to say what strategy Mitsar chose.

Where are your Neutral (N) leads positioned on the head? The Electro-caps put this on AFz, but the headbox shown on the link below has two N jacks. 

http://bio-medical.com/media/support/mitsareegoperationmanual.pdf

http://www.ti.com/lit/an/sbaa188/sbaa188.pdf

you can filter this noise in softwares (such as Matlab).

Thank you again for your valuable input. I have already reduced some A/C noise based on Erik's suggestions.

congrats Efthymios!