Module 8: Introduction to Signals and Systems

Lectures & Content

Folder description

Please click the folder link above to access the Module 8 instructional content. Module 8 contains 11 video lectures that present the following topics:

Fourier Representation of Signals (8A)
Synthesis and Analysis of Signals (8B)
Introduction of Fourier by Power Series (Example 1)
Convergence of the Fourier Series Representation of a Signal (8C)
Fourier Expansion (Example 2)
Filters Operating on LTI Signals (8D)
Properties of Fourier Series (8E)
Convergence and Extreme Optimism Pessimism (Example 3)
1-norm, 2-norm (Example 4)
Circadian Rhythms and Insulin Secretion (8F)
Outline Convergence 1-norm, 2-norm for Fourier Series (Example 5)

Technical

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Module at a Glance ObjectivesHow to Complete This Module:

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Objectives

By the end of this module, you will be able to:

Explain how a signal is represented as a Fourier Series.
Apply Synthesis and Analysis operations for Fourier Series.
Define Convergence Properties for Fourier Expansions.
Describe how Filters work in LTI systems.
Apply Fourier Series to analyze Filters.
Describe Circadian Rhythms and Insulin Secretion.
Apply ideas for analyzing convergence (1-norm, 2-norm) to Fourier Expansions.

How to Complete This Module:

View lectures 8A-8F and Examples 1-5.
Complete the assigned reading to supplement the material presented in the lectures.
Participate in the module discussion.
Complete and submit the module assignment.
Complete the required entry in your personal learning journal.

Technical

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Readings

Cell description

This week's reading assignment includes the following:

Text Books

Astrom, J. K. & Murray, R.M..Feedback systems: An introduction for scientists and engineers. Princeton, NJ: Princeton University Press. (2008).Feedback systems: An introduction for scientists and engineers. Princeton, NJ: Princeton University Press.Available at: http://www.cds.caltech.edu/~murray/amwiki/index.php/Second_Edition

Review: Chapters 1-4
Chaparro, L. (2014). Signals and systems using MATLAB (2nd ed.). Academic Press.
- Chapter 4

EReserves

Boden G, Ruiz J, Urbain JL, & Chen X. (Aug 1996). Evidence for a circadian rhythm of insulin secretion. American Journal of Physiology, 271(2 Pt 1). (This reading accompanies lecture 8F) E246.full.pdf

Technical

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K. &amp; Murray, R.M..<em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.&nbsp;<span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">(2008).</span><em style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: italic; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; color: #444444; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial;\">Feedback systems: An introduction for scientists and engineers</em><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">. Princeton, NJ: Princeton University Press.</span><br style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial;\"><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">Available at:&nbsp;http://www.cds.caltech.edu/~murray/amwiki/index.php/Second_Edition</span></p> \n <ul> \n  <li>Review: Chapters 1-4</li> \n  <li>Chaparro, L. (2014). <em>Signals and systems using MATLAB </em>(2nd ed.). Academic Press. \n   <ul style=\"list-style-type: circle;\"> \n    <li>Chapter 4</li> \n   </ul> </li> \n </ul> \n <p><strong style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px;\"><span style=\"color: #0067ac;\">EReserves</span></strong></p> \n <ul> \n  <li>Boden G, Ruiz J, Urbain JL, &amp; Chen X. (Aug 1996). 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K. &amp; Murray, R.M..<em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.&nbsp;<span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">(2008).</span><em style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: italic; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; color: #444444; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial;\">Feedback systems: An introduction for scientists and engineers</em><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">. Princeton, NJ: Princeton University Press.</span><br style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial;\"><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f4f4f4; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\">Available at:&nbsp;http://www.cds.caltech.edu/~murray/amwiki/index.php/Second_Edition</span></p> \n <ul> \n  <li>Review: Chapters 1-4</li> \n  <li>Chaparro, L. (2014). <em>Signals and systems using MATLAB </em>(2nd ed.). Academic Press. \n   <ul style=\"list-style-type: circle;\"> \n    <li>Chapter 4</li> \n   </ul> </li> \n </ul> \n <p><strong style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px;\"><span style=\"color: #0067ac;\">EReserves</span></strong></p> \n <ul> \n  <li>Boden G, Ruiz J, Urbain JL, &amp; Chen X. (Aug 1996). 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        "body": "\n    <div> \n <p>This week's reading assignment includes the following:</p> \n <p><strong><span>Text Books</span> </strong></p> \n <p>Astrom, J. K. &amp; Murray, R.M..<em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.&nbsp;<span>(2008).</span><em>Feedback systems: An introduction for scientists and engineers</em><span>. Princeton, NJ: Princeton University Press.</span><span>Available at:&nbsp;http://www.cds.caltech.edu/~murray/amwiki/index.php/Second_Edition</span></p> \n <ul> \n  <li>Review: Chapters 1-4</li> \n  <li>Chaparro, L. (2014). <em>Signals and systems using MATLAB </em>(2nd ed.). Academic Press. \n   <ul> \n    <li>Chapter 4</li> \n   </ul> </li> \n </ul> \n <p><strong><span>EReserves</span></strong></p> \n <ul> \n  <li>Boden G, Ruiz J, Urbain JL, &amp; Chen X. (Aug 1996). Evidence for a circadian rhythm of insulin secretion. <em>American Journal of Physiology,</em> 271(2 Pt 1).&nbsp;(This reading accompanies lecture 8F)&nbsp;\n<a alt=\"\" href=\"https://blackboard.jhu.edu/bbcswebdav/pid-5740811-dt-content-rid-51355329_2/xid-51355329_2\" target=\"_blank\">E246.full.pdf</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.260.81.FA18/E246.full.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00uv&amp;course_id=_169707_1&amp;ctxMenuXythosId=51355329_2&amp;course_id=_169707_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_678ab7c3992c44c39c9f0dc2705f9141,open_with_browser_678ab7c3992c44c39c9f0dc2705f9141,open_with_bbdrive_678ab7c3992c44c39c9f0dc2705f9141,openWebId_678ab7c3992c44c39c9f0dc2705f9141,view360Id_678ab7c3992c44c39c9f0dc2705f9141,*separator*,*separator*,ax-ally-placeholder_678ab7c3992c44c39c9f0dc2705f9141,ax-ally-markForAxAnalysis_678ab7c3992c44c39c9f0dc2705f9141,*separator*,*separator*,content_settings_678ab7c3992c44c39c9f0dc2705f9141,content_editSettings_678ab7c3992c44c39c9f0dc2705f9141,content_edit_678ab7c3992c44c39c9f0dc2705f9141,properties_folder_678ab7c3992c44c39c9f0dc2705f9141,itemcarot_managerecord_678ab7c3992c44c39c9f0dc2705f9141,comments_tool_678ab7c3992c44c39c9f0dc2705f9141,subscriptions_list_678ab7c3992c44c39c9f0dc2705f9141,content_readfile_678ab7c3992c44c39c9f0dc2705f9141,content_overwrite_678ab7c3992c44c39c9f0dc2705f9141,passes_tool_678ab7c3992c44c39c9f0dc2705f9141,permissions_tool_678ab7c3992c44c39c9f0dc2705f9141,content_add_alignment_678ab7c3992c44c39c9f0dc2705f9141,content_tracking_678ab7c3992c44c39c9f0dc2705f9141,content_versions_678ab7c3992c44c39c9f0dc2705f9141,*separator*,*separator*,bookmarkId_678ab7c3992c44c39c9f0dc2705f9141,itemsId_678ab7c3992c44c39c9f0dc2705f9141,packagesId_678ab7c3992c44c39c9f0dc2705f9141,emailId_678ab7c3992c44c39c9f0dc2705f9141,removeContentFolderId_678ab7c3992c44c39c9f0dc2705f9141,*separator*,copyContentId_678ab7c3992c44c39c9f0dc2705f9141,moveContentId_678ab7c3992c44c39c9f0dc2705f9141,*separator*,removeContentId_678ab7c3992c44c39c9f0dc2705f9141,*separator*,Metadata_General_678ab7c3992c44c39c9f0dc2705f9141,Metadata_Dublin_Core_678ab7c3992c44c39c9f0dc2705f9141,Metadata_IMS_678ab7c3992c44c39c9f0dc2705f9141,Metadata_Full_IMS_678ab7c3992c44c39c9f0dc2705f9141,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_678ab7c3992c44c39c9f0dc2705f9141\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_678ab7c3992c44c39c9f0dc2705f9141',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_678ab7c3992c44c39c9f0dc2705f9141',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n  </span> \n \n \n \n \n \n&nbsp;</li> \n </ul> \n</div>\n  "
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Module 8 Discussion Participation GuidelinesQuestion:

Cell description

Discussion forum rubric: 625.260 Discusssion Rubric

Participation Guidelines

Participation in class discussions are important in this course and to your final grade. Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.

Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.

There is one discussion thread in this module. Submit your posts by clicking on the "Module 8 Discussion" link above and creating a new thread. Please contribute to the class discussion with your discussion about:

Question:

Thread 8.1

Have you worked with Fourier Series before?
Have you experienced the ‘Dawn Phenomena’ described in this week’s paper about insulin?
Give an example of a problem where you think Fourier Series provided you with new insights into the solution (feel free to search the web if you don’t have prior problems).

For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.

Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.

You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.

Required Activity: 1 Original Post / 2 Responses Due by: Original Post 11:59PM Day 4, Responses 11:59PM Day 7

Technical

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Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.</p> \n <p style=\"margin-left: 30px;\">Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.&nbsp;</p> \n <p style=\"margin-left: 30px;\">There is one discussion thread in this module. Submit your posts by clicking on the \"Module 8 Discussion\" link above and creating a new thread. Please contribute to the class discussion with your discussion about:</p> \n <h3 style=\"color: #0067ac;\" id=\"anonymous_element_15\">Question:</h3> \n <p style=\"margin-left: 30px;\"><strong style=\"font-size: 13px;\">Thread 8.1</strong></p> \n <ul style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"> \n  <li style=\"font-size: 13px;\">Have you worked with Fourier Series before?</li> \n  <li style=\"font-size: 13px;\">Have you experienced the ‘Dawn Phenomena’ described in this week’s paper about insulin?</li> \n  <li style=\"font-size: 13px;\">Give an example of a problem where you think Fourier Series provided you with new insights into the solution (feel free to search the web if you don’t have prior problems).</li> \n </ul> \n <p style=\"margin-left: 30px;\">For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.</p> \n <p style=\"margin-left: 30px;\">Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.</p> \n <p style=\"margin-left: 30px;\">You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.</p> \n <p style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"><span style=\"text-decoration: underline;\">Required Activity</span>: 1 Original Post / 2 Responses<br> <span style=\"text-decoration: underline;\">Due by</span>: Original Post 11:59PM Day 4, Responses 11:59PM Day 7</p> \n <br> \n</div>\n  </div>\n\n <div id=\"_5740812_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.</p> \n <p style=\"margin-left: 30px;\">Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.&nbsp;</p> \n <p style=\"margin-left: 30px;\">There is one discussion thread in this module. Submit your posts by clicking on the \"Module 8 Discussion\" link above and creating a new thread. 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This is how we will build a community around the course.</p> \n <p style=\"margin-left: 30px;\">You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.</p> \n <p style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"><span style=\"text-decoration: underline;\">Required Activity</span>: 1 Original Post / 2 Responses<br> <span style=\"text-decoration: underline;\">Due by</span>: Original Post 11:59PM Day 4, Responses 11:59PM Day 7</p> \n <br> \n</div>\n  </div>\n\n <div id=\"_5740812_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Module 8 Assignment

Cell description

In this module, you will complete the problem sets listed below as an assignment:

Chaparro: problems 4.24, 4.25, 4.26 (2nd edition)

Follow the general guidelines below to complete and submit the assignment.

Problems should be done neatly on paper and scanned or completed electronically using markup on a tablet device.
At the top of the page, include your name, module number, and page number (page 1 of 2, etc.)
Submit your answers in PDF (.pdf) format by uploading to Blackboard using the "Module 8 Assignment" link above.

Required Activity: Submit answers to the problem sets. Due by: 11:59 PM Day

Technical

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Module 8 Personal Learning Journal

Cell description

In your learning journal entries for this week comment about:

How Fourier Series can contribute to your project and/or your long-term goals?
Work more on your project ideas and how they might best be implemented.

Click on the “Module 8 Personal Learning Journal” above to access your journal and create your entry.

Required Activity: Create a reflective personal journal entry post in response to the prompts given.Due by: 11:59 PM Day 7

Technical

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