Physics A-Level Digital Signals Notes

… Analogue signals are continuous – they can take any value between some minimum and maximum.

… Digital signals can only be ‘high’ (1) or ‘low’ (0)

… To transmit a signal over a distance, it is necessary to amplify the signal at various stages. With an analogue signal, you will end up amplifying the noise (interference). This noise can be filtered out, but you will lose detail in the original signal.
However, with a digital signal, the noise is eliminated (because it is much easier to see when a signal should be a ‘1’ or a ‘0’), and the original signal is regenerated perfectly.

… Analogue to digital conversion is required when ‘sampling’ an analogue waveform and converting it into a stream of 0s and 1s.

… The number of quantisation levels refers to how many different levels can be coded from the signal. If the levels are too large, then you will see quantisation errors occus where the nearest quantisation level is significantly far from the signal level.

… The number of quantisation levels = 2^b , where b is the number of bits used per sample.

… The resolution of a sample is the smallest change in the signal (e.g. potential difference) that can be determined. 
Resolution = Potential difference range of signal / Number of quantisation levels

… It is often not useful to encode noise that might be in the original signal to be sampled:
The maximum useful number of levels = total signal range (including noise) / noise range = V(total) / V(noise)

This leads to the number of bits per sample, b:
b = log(base2) [ V(total)/V(noise) ]

… When sampling a signal, the minimum sampling rate = 2 x the highest frequency in the signal. This is to ensure that the highest frequencies are still ‘captured’ in the sampling process. 
‘Aliasing’ can occur if this is not the case (unwanted low frequencies).

… Bit rate (Hz or /s) = samples per second  x  bits per sec