A DSP system has three fundamental sources of limitation:
 loss of information because we only take samples of the signal at intervals
 loss of information because we only sample the signal for a certain length of time
 errors due to limited precision (ie word length) in data storage and arithmetic
The effects of these limitations are as follows:
 aliasing is the result of sampling, which means we cannot distinguish between high and low frequencies
 limited frequency resolution is the result of limited duration of sampling, which means we cannot distinguish between adjacent frequencies
 quantisation error is the result of limited precision (word length) when converting between analogue and digital forms, when storing data, or when performing arithmetic
Aliasing and frequency resolution are fundamental limitations  they arise from the mathematics and cannot be overcome. They are limitations of any sampled data system, not just digital ones.
Quantisation error is an artifact of the imperfect precision, and can be improved upon by using an increased word length. It is a feature peculiar to digital systems. Its effects are non linear and signal dependent, but can sometimes be acceptably modelled as injections of random noise.
