Problem analysis is done during systems analysis phase.
Prototyping is an iterative process that is part of the analysis phase of the system development life cycle. During this analysis phase, prototyping usually referred to as the discovery prototypes are very important because it is geared for understanding the users' needs.
The analysis phase defines the requirements of the system, independent of how these requirements will be accomplished. This phase defines the problem that the customer is trying to solve.
The system analyst is a person who is thoroughly aware of the system and guides the system development project by giving proper directions. He is an expert having technical and interpersonal skills to carry out development tasks required at each phase.
System analysis as a problem-solving technique that breaks down a system into its component pieces for the purpose of the studying how well those component parts work and interact to accomplish their purpose.