Unit 2: Signals and Systems

Linear Time-Invariant Signals and Systems

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Session Overview

 Diagram of feedback addition composition.

In the last session, we demonstrated the versatility of state machines and introduced signals and systems. In this session, we will focus on linear time-invariant (LTI) systems. We’ll be able to represent LTI systems using state machines, and introduce other ways to represent LTI systems. Once we know that a system is LTI, we can use what we know about linear time-invariance to analyze and predict the behavior of the system.

The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand (theory) and be able to do (practice) after completing this session, and additional resources.

Session Content


Read sections 5.1-5.4 of the course notes.

Recitation Video

These videos have been developed for OCW Scholar, and are designed to supplement the lecture videos.

Session Activities

The problems in the tables below are taken from the 6.01 Online Tutor, an interactive environment that is not available on OCW. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

Software Lab

4.1.1 Constructing signals (PDF)
4.1.2 Step signal (PDF)
4.1.3 Subclasses of signals (PDF)
4.1.4 Additional subclasses (PDF)
4.1.5 PolyR on signals (PDF)

Design Lab

Do problem 4.2.1 before the design lab.

4.2.1 Difference equations (PDF)
4.3.1 Wall finder (PDF)
4.3.3 State machine composition (PDF)
4.3.5 Wall finder state machine (PDF)
4.3.6 Wall finder gains (PDF)

Additional Exercises

4.4.1 LTISM (PDF)
4.4.2 Implement LTISM (PDF)
4.4.3 TransducedSignal (PDF)

Check Yourself


Nano-quiz problems and solutions are taken from a previous version of the 6.01 Online Tutor. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

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Learning Resource Types
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theaters Recitation Videos
assignment Problem Sets
grading Exams with Solutions
notes Lecture Notes
menu_book Online Textbook
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