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Noise may be generated within the electrical components of the input amplifier: internal noise. It may also be added to the signal as it travels down the input wires to the amplifier: external noise.
Internal noise arises from thermal effects in the amplifier and although it can be minimised it cannot be removed completely. Typically amplifiers will generate a few microvolts of internal noise which limits the resolution of the signal to this level. The amount of noise added to the signal depends on the bandwidth of the input amplifier (from the lowest frequency allowed into the amplifier to the highest). Amplifiers with a bandwidth reduced to the bandwidth of the input signal will be less noisy than, say, feeding a 100 Hz signal into an amplifier that covers 0 to 10 MHz. Integrating A-D converters reduce noise by integrating the signal over a period, which is effectively reducing the bandwidth.
External noise reduction is much more of an art form. Noise is added because the signal leads act as aerials picking up environmental electrical activity. A lot of this is common to both signal wires and a differential amplifier will remove a lot of common mode voltage. Differences between the signal wires (for example if they are separated rather than twisted together) will lead to residual voltages being added to the signal, increasing noise. Keeping the signal wires as short as possible, and as far away from electrical machinery as possible, will help.
Filtering also reduces noise errors in the signal. For most applications a low-pass filter is used. This allows through the lower frequency components but attenuates the higher frequencies. The cut-off frequency must be compatible with the frequencies present in the actual signal (as opposed to possible contamination by noise) and the sampling rate used for the A-D conversion.
A low-pass filter that's used to prevent higher frequencies, in either the signal or noise, from introducing distortion into the digitised signal is known as an anti-aliasing filter. These generally have a sharper cut-off than the normal low-pass filter used to condition a signal. Anti-aliasing filters are specified according to the sampling rate of the system and there must be one filter per input signal.
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