The unit introduces the theory and practice of signals and linear systems and shows how transform techniques and transfer functions can be used to solve problems in several engineering fields. This unit forms the basis for Control Theory required for future control units. Harmonic analysis, signal decomposition and transforms are treated in a logical sequence showing their inter-relationship. Similarly, digital systems and transforms will be derived from sampling theory, converting analog systems and continuous transforms to equivalent digital systems, and thus show their inter-relationship. Special emphasis is placed on the use and proficient application of higher mathematics. This includes complex analysis, matrix representation and solution, and liberal use is made of linear algebra and the state space representation and solution methodology. The unit introduces the student to stochastic systems analysis and the predictability of observable phenomena. These ideas and theory are important for an understanding of renewable energy resources and their limitations, and to characterize the reliability of energy sources. Liberal use is made of the concept of an expectation value – including the differences between the definition of the expectation value on the time domain and the ensemble or space domain. Thus the student is led to an understanding of these aspects via a special emphasis on the Ergodic theorem. Special conditions leading to weak forms of the Ergodic theorem is studied with practical examples. The student will be able to design complex systems making use of the concepts learned, in practical and real world problems. There are three detailed written tests/examinations during the semester that assess the student’s mastery of learning outcomes. Students are assumed to have knowledge in mathematics including complex number and linear algebra.