## Signals and Systems ILOs for Unified Engineering (16.01-16.04)

### Intended Learning Outcomes

Students graduating from 16.030/040 will be able to:

1. Demonstrate an understanding of the fundamental properties of linear systems, by explaining the properties to others.
2. Use linear systems tools, especially transform analysis and convolution, to analyze and predict the behavior of linear systems
3. Gain an appreciation for the importance of linear systems analysis in aerospace systems.

### Measurable Outcomes (assessment method)

Students graduating from 16.030/040 will be able to:

1. Explain the importance of superposition in the analysis of linear systems. (concept test, homework, quiz)
2. Explain the role of convolution in the analysis of linear time invariant systems, and use convolution to determine the response of linear systems to arbitrary inputs. (concept test, homework, quiz)
3. List and apply properties of the unilateral and bilateral Laplace transforms. (concept test, homework, quiz)
4. Use Laplace transforms to solve differential equations, and to determine the response of linear systems to known inputs. (homework, quiz)
5. Demonstrate an understanding of the relationship between the stability and causality of systems and the region of convergence of their Laplace transforms, by correctly explaining the relationship, and using the relationship to determine the stability and causality of systems. (concept test, homework, quiz)
6. Demonstrate an understanding of the relation among the transfer function, convolution, and the impulse response, by explaining the relationship, and using the relationship to solve forced response problems. (concept test, homework, quiz)
7. Explain the relationship between a signal’s bandwidth and its duration, and use that relationship to predict and explain the bandwidth requirements for aerospace applications such as Loran navigation, amplitude modulation, etc. (homework, quiz)
8. Explain the fundamentals of modulation, including amplitude modulation, frequency modulation, and sampling (impulse modulation), including the implications of the sampling theorem. (homework, quiz)