Module 9: Introduction to Signals and Systems

Lectures & Content

Folder description

Please click the folder link above to access the Module 9 instructional content. Module 9 contains 12 video lectures that present the following topics:

Introduction to Fourier Transform (9A)
Connections Between Fourier and Laplace Transforms (9B)
Introduction to Heat Equation and its Solution by Fourier Transform (Example 1)
Modulation and Convolution (9C)
Fourier Transform of the Heat Equation (Example 2)
Filtering, Poles, and Zeros for Special Analysis (9D)
Fourier Transform for Infrared Spectroscopy (9E)
Convolution and the Transform (Example 3)
Diffusion Equation and Image Analysis (Example 4)
Non-Invasive Glucose Monitoring (9F)
Anisotropic Diffusion // Parseval's Theorem (Example 5)
Properties of the Fourier Transform (9G)

Technical

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Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

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

Explain how Fourier and Laplace Transforms are related.
Apply the ideas of Poles and Zeros in a Transfer Function.
Define Convolution in the setting of the Fourier Transform.
Describe how the Fourier Transform helps with spectroscopy.
Apply the Fourier Transform to solve the heat/diffusion equation.
Describe how spectral methods might lead to non-invasive glucose monitors.
Apply the properties of the Fourier Transform to image analysis.

How to Complete This Module:

View lectures 9A-9G 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. (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 5

EReserves

Baker, M. J., Trevisan, J., Bassan, P. et. al. (3 Jul 2014). Using Fourier transform IR spectroscopy to analyze biological materials. Nature Protocols 9(8) pp. 1771-1791.
Introduction to Fourier Transform Infrared Spectrometry (2001). Thermo Nicolet Corporation.
Yadava, J., Rania, A., Singha, V., & Mohan Murarib, B. (2015). Prospects and limitations of non-invasive blood glucose monitoring using near-infrared spectroscopy. Biomedical Signal Processing and Control 18 (2015) pp. 214–227.
Quantified Health (8 Aug 2015). A non-invasive blood glucose tracking device is being developed by Sano. http://quantifiedhealth.blogspot.com/2015/07/a-non-invasive-blood-glucose-tracking.html

Technical

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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;\">/Second_Edition</span> \n   <ul style=\"list-style-type: circle;\"> \n    <li>Review: Chapters 1-4</li> \n   </ul> </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 5</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>Baker, M. J., Trevisan, J., Bassan, P. et. al. (3 Jul 2014). Using Fourier transform IR spectroscopy to analyze biological materials. <em>Nature Protocols</em> 9(8) pp. 1771-1791.</li> \n  <li>Introduction to Fourier Transform Infrared Spectrometry (2001). <em>Thermo Nicolet Corporation.</em></li> \n  <li>Yadava, J., Rania, A., Singha, V., &amp; Mohan Murarib, B. (2015). Prospects and limitations of non-invasive blood glucose monitoring using near-infrared spectroscopy. <em>Biomedical Signal Processing and Control</em> 18 (2015) pp. 214–227.</li> \n  <li>Quantified Health (8 Aug 2015). A non-invasive blood glucose tracking device is being developed by Sano. http://quantifiedhealth.blogspot.com/2015/07/a-non-invasive-blood-glucose-tracking.html</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_5740829_1previewModule\" class=\"moduleSample\">\n </div>\n",
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    "html": "\n\n<img alt=\"Tools Area\" src=\"/webapps/ATLS-AresCourseReserves-bb_bb60/images/ares.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_5740829_1\">\n\n <h3 id=\"anonymous_element_12\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_169707_1&amp;content_id=_5740829_1&amp;mode=view\"><span style=\"color:#0067AC;\">Readings</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_5740829_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Readings\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>This week's reading assignment includes the following:</p> \n <p><strong><span style=\"color: #0067ac;\">Text Books</span> </strong></p> \n <ul> \n  <li>Astrom, J. K. &amp; Murray, R.M. (2008).<em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.<br>Available at:&nbsp;<span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">http</span><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;\">://</span><span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">www</span><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;\">.</span><span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">cds</span><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;\">.</span><span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">caltech</span><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;\">.</span><span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">edu</span><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;\">/</span><span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">~murray</span><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;\">/</span><span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">amwiki</span><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;\">/index.</span><span style=\"margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: normal; font-style: normal; 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;\">php</span><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;\">/Second_Edition</span> \n   <ul style=\"list-style-type: circle;\"> \n    <li>Review: Chapters 1-4</li> \n   </ul> </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 5</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>Baker, M. J., Trevisan, J., Bassan, P. et. al. (3 Jul 2014). Using Fourier transform IR spectroscopy to analyze biological materials. <em>Nature Protocols</em> 9(8) pp. 1771-1791.</li> \n  <li>Introduction to Fourier Transform Infrared Spectrometry (2001). <em>Thermo Nicolet Corporation.</em></li> \n  <li>Yadava, J., Rania, A., Singha, V., &amp; Mohan Murarib, B. (2015). Prospects and limitations of non-invasive blood glucose monitoring using near-infrared spectroscopy. <em>Biomedical Signal Processing and Control</em> 18 (2015) pp. 214–227.</li> \n  <li>Quantified Health (8 Aug 2015). A non-invasive blood glucose tracking device is being developed by Sano. http://quantifiedhealth.blogspot.com/2015/07/a-non-invasive-blood-glucose-tracking.html</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_5740829_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Readings",
        "body": "\n    <div> \n <p>This week's reading assignment includes the following:</p> \n <p><strong><span>Text Books</span> </strong></p> \n <ul> \n  <li>Astrom, J. K. &amp; Murray, R.M. (2008).<em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.Available at:&nbsp;<span>http</span><span>://</span><span>www</span><span>.</span><span>cds</span><span>.</span><span>caltech</span><span>.</span><span>edu</span><span>/</span><span>~murray</span><span>/</span><span>amwiki</span><span>/index.</span><span>php</span><span>/Second_Edition</span> \n   <ul> \n    <li>Review: Chapters 1-4</li> \n   </ul> </li> \n  <li>Chaparro, L. (2014). <em>Signals and systems using MATLAB </em>(2nd ed.). Academic Press. \n   <ul> \n    <li>Chapter 5</li> \n   </ul> </li> \n </ul> \n <p><strong><span>EReserves</span></strong></p> \n <ul> \n  <li>Baker, M. J., Trevisan, J., Bassan, P. et. al. (3 Jul 2014). Using Fourier transform IR spectroscopy to analyze biological materials. <em>Nature Protocols</em> 9(8) pp. 1771-1791.</li> \n  <li>Introduction to Fourier Transform Infrared Spectrometry (2001). <em>Thermo Nicolet Corporation.</em></li> \n  <li>Yadava, J., Rania, A., Singha, V., &amp; Mohan Murarib, B. (2015). Prospects and limitations of non-invasive blood glucose monitoring using near-infrared spectroscopy. <em>Biomedical Signal Processing and Control</em> 18 (2015) pp. 214–227.</li> \n  <li>Quantified Health (8 Aug 2015). A non-invasive blood glucose tracking device is being developed by Sano. http://quantifiedhealth.blogspot.com/2015/07/a-non-invasive-blood-glucose-tracking.html</li> \n </ul> \n</div>\n  "
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Module 9 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 9.1

Have you worked with the Fourier Transform before?
What is your sense about the chances for non-invasive glucose monitors to be on the market soon?
Give an example of a problem where you think Fourier Transform methods may provide 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 9.1</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 the Fourier Transform before?</li> \n  <li style=\"font-size: 13px;\">What is your sense about the chances for non-invasive glucose monitors to be on the market soon?</li> \n  <li style=\"font-size: 13px;\">Give an example of a problem where you think Fourier Transform methods may provide 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 <p style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"></p> \n <br> \n</div>\n  </div>\n\n <div id=\"_5740830_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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Module 9 Assignment

Cell description

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

Chaparro: problems 5.29, 5.30, 5.31 (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 9 Assignment" link above.

Required Activity: Submit answers to the problem sets. Due by: 11:59 PM Day 7

Technical

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Module 9 Personal Learning Journal

Cell description

In your learning journal entries for this week comment about:

How Fourier Transforms 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 9 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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    "html": "\n\n<img alt=\"Journals\" src=\"/images/ci/sets/set01/journal_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_5740832_1\">\n\n <h3 id=\"anonymous_element_17\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_169707_1&amp;content_id=_5740832_1&amp;mode=view\"><span style=\"color:#0067ac;\">Module 9 Personal Learning Journal</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_5740832_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Module 9 Personal Learning Journal\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>In your learning journal entries for this week comment about:</p> \n <ul> \n  <li>How Fourier Transforms can contribute to your project and/or your long-term goals?</li> \n  <li>Work more on your project ideas and how they might best be implemented.</li> \n </ul> \n <p>Click on the “Module 9 Personal Learning Journal” above to access your journal and create your entry.</p> \n <p><span style=\"text-decoration: underline;\">Required Activity</span>: Create a reflective personal journal entry post in response to the prompts given.<br> <span style=\"text-decoration: underline;\">Due by</span>: 11:59 PM Day 7</p> \n</div>\n  </div>\n\n <div id=\"_5740832_1previewModule\" class=\"moduleSample\">\n </div>\n",
    "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_169707_1&content_id=_5740832_1&mode=view",
    "parent": 131,
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    "rendered": {
        "title": "Module 9 Personal Learning Journal",
        "body": "\n    <div> \n <p>In your learning journal entries for this week comment about:</p> \n <ul> \n  <li>How Fourier Transforms can contribute to your project and/or your long-term goals?</li> \n  <li>Work more on your project ideas and how they might best be implemented.</li> \n </ul> \n <p>Click on the “Module 9 Personal Learning Journal” above to access your journal and create your entry.</p> \n <p><span>Required Activity</span>: Create a reflective personal journal entry post in response to the prompts given. <span>Due by</span>: 11:59 PM Day 7</p> \n</div>\n  "
    },
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}