Module 7: Fourier Transforms

Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

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

  • Utilize different forms of Fourier transforms, particularly for functions over R and Z, and for the case of periodic functions over R.
  • Apply residue integration and other techniques of complex analysis.
  • Utilize the Poisson Sum Formula and Payley-Wiener theorem.

How to Complete This Module:

  1. View the video lectures in sequence.
  2. Read the Assignment 7 problems. Note that the problem labeled in boldface (on sampling and the Fourier series) extends some of the concepts discussed in the lectures.
  3. Read the Lecture Notes that accompany the module. As you read the notes, identify points that will help you do the problems.
  4. Submit the Assignment 7 problems. As you work on them:
    • Ask questions in Piazza.
    • Refer to the notes and the textbook, or review certain videos as necessary.
    • You may find that you need to review some topics covered in prior modules (e.g., residue methods). It is important to pose questions to the instructor who can guide you through a review process if it is necessary.
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Readings

Cell description
  • Stein, E, & Shakarchi, R. (2003). Complex analysis. Princeton University Press.
    • Chapter 4 (optional)
  • Module 7 Lecture Notes (PDF) : Read the Lecture Notes at least once through. Some of the more technical points regarding proofs may be a bit challenging, but the experience gained in reading through those sections at least once is worthwhile.
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Video Lectures

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src=\"https://www.kaltura.com/p/1458241/sp/145824100/embedIframeJs/uiconf_id/16721441/partner_id/1458241/widget_id/1_bdqwtmed?iframeembed=true&amp;playerId=kaltura_player_&amp;flashvars[playlistAPI.kpl0Id]=1_gsn3zret&amp;flashvars[ks]=&amp;&amp;flashvars[imageDefaultDuration]=30&amp;flashvars[localizationCode]=en&amp;flashvars[leadWithHTML5]=true&amp;flashvars[forceMobileHTML5]=true&amp;flashvars[nextPrevBtn.plugin]=true&amp;flashvars[sideBarContainer.plugin]=true&amp;flashvars[sideBarContainer.position]=left&amp;flashvars[sideBarContainer.clickToClose]=true&amp;flashvars[chapters.plugin]=true&amp;flashvars[chapters.layout]=vertical&amp;flashvars[chapters.thumbnailRotator]=false&amp;flashvars[streamSelector.plugin]=true&amp;flashvars[EmbedPlayer.SpinnerTarget]=videoHolder&amp;flashvars[dualScreen.plugin]=true&amp;flashvars[playlistAPI.playlistUrl]=https://kaf.ep.jhu.edu/playlist/details/{playlistAPI.kpl0Id}/categoryid/165308111\" allowfullscreen=\"\" webkitallowfullscreen=\"\" 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bb:contextparameters=\"\" 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data-ally-scoreindicator=\"_90880949_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880949_2/xid-90880949_2\" target=\"_blank\" rel=\"noreferrer noopener\">07B_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07B_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00ix&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880949_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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data-ally-scoreindicator=\"_90880951_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880951_2/xid-90880951_2\" target=\"_blank\" rel=\"noreferrer noopener\">07D_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07D_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j1&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880951_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_cadc939cddfc4280b060bfac42c30e08\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"90880951_2_fileReadWritePermAvl\" id=\"90880951_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('cadc939cddfc4280b060bfac42c30e08');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880952_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880952_2/xid-90880952_2\" target=\"_blank\" rel=\"noreferrer noopener\">07E_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j3&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880952_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_2717c401524546a18def931e58dd7fd0,open_with_browser_2717c401524546a18def931e58dd7fd0,open_with_bbdrive_2717c401524546a18def931e58dd7fd0,openWebId_2717c401524546a18def931e58dd7fd0,view360Id_2717c401524546a18def931e58dd7fd0,*separator*,*separator*,ax-ally-placeholder_2717c401524546a18def931e58dd7fd0,ax-ally-markForAxAnalysis_2717c401524546a18def931e58dd7fd0,*separator*,*separator*,content_settings_2717c401524546a18def931e58dd7fd0,content_editSettings_2717c401524546a18def931e58dd7fd0,content_edit_2717c401524546a18def931e58dd7fd0,properties_folder_2717c401524546a18def931e58dd7fd0,itemcarot_managerecord_2717c401524546a18def931e58dd7fd0,comments_tool_2717c401524546a18def931e58dd7fd0,subscriptions_list_2717c401524546a18def931e58dd7fd0,content_readfile_2717c401524546a18def931e58dd7fd0,content_overwrite_2717c401524546a18def931e58dd7fd0,passes_tool_2717c401524546a18def931e58dd7fd0,permissions_tool_2717c401524546a18def931e58dd7fd0,content_add_alignment_2717c401524546a18def931e58dd7fd0,content_tracking_2717c401524546a18def931e58dd7fd0,content_versions_2717c401524546a18def931e58dd7fd0,*separator*,*separator*,bookmarkId_2717c401524546a18def931e58dd7fd0,itemsId_2717c401524546a18def931e58dd7fd0,packagesId_2717c401524546a18def931e58dd7fd0,emailId_2717c401524546a18def931e58dd7fd0,removeContentFolderId_2717c401524546a18def931e58dd7fd0,*separator*,copyContentId_2717c401524546a18def931e58dd7fd0,moveContentId_2717c401524546a18def931e58dd7fd0,*separator*,removeContentId_2717c401524546a18def931e58dd7fd0,*separator*,Metadata_General_2717c401524546a18def931e58dd7fd0,Metadata_Dublin_Core_2717c401524546a18def931e58dd7fd0,Metadata_IMS_2717c401524546a18def931e58dd7fd0,Metadata_Full_IMS_2717c401524546a18def931e58dd7fd0,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_2717c401524546a18def931e58dd7fd0\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_2717c401524546a18def931e58dd7fd0',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_2717c401524546a18def931e58dd7fd0',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_2717c401524546a18def931e58dd7fd0',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"90880952_2_fileReadWritePermAvl\" id=\"90880952_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('2717c401524546a18def931e58dd7fd0');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880953_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880953_2/xid-90880953_2\" target=\"_blank\" rel=\"noreferrer noopener\">07F_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07F_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j5&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880953_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_c28d154f3f244322a3bec16e2f784dde,open_with_browser_c28d154f3f244322a3bec16e2f784dde,open_with_bbdrive_c28d154f3f244322a3bec16e2f784dde,openWebId_c28d154f3f244322a3bec16e2f784dde,view360Id_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,ax-ally-placeholder_c28d154f3f244322a3bec16e2f784dde,ax-ally-markForAxAnalysis_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,content_settings_c28d154f3f244322a3bec16e2f784dde,content_editSettings_c28d154f3f244322a3bec16e2f784dde,content_edit_c28d154f3f244322a3bec16e2f784dde,properties_folder_c28d154f3f244322a3bec16e2f784dde,itemcarot_managerecord_c28d154f3f244322a3bec16e2f784dde,comments_tool_c28d154f3f244322a3bec16e2f784dde,subscriptions_list_c28d154f3f244322a3bec16e2f784dde,content_readfile_c28d154f3f244322a3bec16e2f784dde,content_overwrite_c28d154f3f244322a3bec16e2f784dde,passes_tool_c28d154f3f244322a3bec16e2f784dde,permissions_tool_c28d154f3f244322a3bec16e2f784dde,content_add_alignment_c28d154f3f244322a3bec16e2f784dde,content_tracking_c28d154f3f244322a3bec16e2f784dde,content_versions_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,bookmarkId_c28d154f3f244322a3bec16e2f784dde,itemsId_c28d154f3f244322a3bec16e2f784dde,packagesId_c28d154f3f244322a3bec16e2f784dde,emailId_c28d154f3f244322a3bec16e2f784dde,removeContentFolderId_c28d154f3f244322a3bec16e2f784dde,*separator*,copyContentId_c28d154f3f244322a3bec16e2f784dde,moveContentId_c28d154f3f244322a3bec16e2f784dde,*separator*,removeContentId_c28d154f3f244322a3bec16e2f784dde,*separator*,Metadata_General_c28d154f3f244322a3bec16e2f784dde,Metadata_Dublin_Core_c28d154f3f244322a3bec16e2f784dde,Metadata_IMS_c28d154f3f244322a3bec16e2f784dde,Metadata_Full_IMS_c28d154f3f244322a3bec16e2f784dde,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_c28d154f3f244322a3bec16e2f784dde\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_c28d154f3f244322a3bec16e2f784dde',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_c28d154f3f244322a3bec16e2f784dde',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_c28d154f3f244322a3bec16e2f784dde',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"90880953_2_fileReadWritePermAvl\" id=\"90880953_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('c28d154f3f244322a3bec16e2f784dde');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880943_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880943_2/xid-90880943_2\" target=\"_blank\" rel=\"noreferrer noopener\">07G_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07G_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j7&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880943_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_2796f09fdfd547049a847f2288e32fee,open_with_browser_2796f09fdfd547049a847f2288e32fee,open_with_bbdrive_2796f09fdfd547049a847f2288e32fee,openWebId_2796f09fdfd547049a847f2288e32fee,view360Id_2796f09fdfd547049a847f2288e32fee,*separator*,*separator*,ax-ally-placeholder_2796f09fdfd547049a847f2288e32fee,ax-ally-markForAxAnalysis_2796f09fdfd547049a847f2288e32fee,*separator*,*separator*,content_settings_2796f09fdfd547049a847f2288e32fee,content_editSettings_2796f09fdfd547049a847f2288e32fee,content_edit_2796f09fdfd547049a847f2288e32fee,properties_folder_2796f09fdfd547049a847f2288e32fee,itemcarot_managerecord_2796f09fdfd547049a847f2288e32fee,comments_tool_2796f09fdfd547049a847f2288e32fee,subscriptions_list_2796f09fdfd547049a847f2288e32fee,content_readfile_2796f09fdfd547049a847f2288e32fee,content_overwrite_2796f09fdfd547049a847f2288e32fee,passes_tool_2796f09fdfd547049a847f2288e32fee,permissions_tool_2796f09fdfd547049a847f2288e32fee,content_add_alignment_2796f09fdfd547049a847f2288e32fee,content_tracking_2796f09fdfd547049a847f2288e32fee,content_versions_2796f09fdfd547049a847f2288e32fee,*separator*,*separator*,bookmarkId_2796f09fdfd547049a847f2288e32fee,itemsId_2796f09fdfd547049a847f2288e32fee,packagesId_2796f09fdfd547049a847f2288e32fee,emailId_2796f09fdfd547049a847f2288e32fee,removeContentFolderId_2796f09fdfd547049a847f2288e32fee,*separator*,copyContentId_2796f09fdfd547049a847f2288e32fee,moveContentId_2796f09fdfd547049a847f2288e32fee,*separator*,removeContentId_2796f09fdfd547049a847f2288e32fee,*separator*,Metadata_General_2796f09fdfd547049a847f2288e32fee,Metadata_Dublin_Core_2796f09fdfd547049a847f2288e32fee,Metadata_IMS_2796f09fdfd547049a847f2288e32fee,Metadata_Full_IMS_2796f09fdfd547049a847f2288e32fee,\" 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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('2796f09fdfd547049a847f2288e32fee');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880944_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880944_2/xid-90880944_2\" target=\"_blank\" rel=\"noreferrer noopener\">07H_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07H_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j9&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880944_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_2ff42bfc8f6c41c0bb8359a8006de4d0,open_with_browser_2ff42bfc8f6c41c0bb8359a8006de4d0,open_with_bbdrive_2ff42bfc8f6c41c0bb8359a8006de4d0,openWebId_2ff42bfc8f6c41c0bb8359a8006de4d0,view360Id_2ff42bfc8f6c41c0bb8359a8006de4d0,*separator*,*separator*,ax-ally-placeholder_2ff42bfc8f6c41c0bb8359a8006de4d0,ax-ally-markForAxAnalysis_2ff42bfc8f6c41c0bb8359a8006de4d0,*separator*,*separator*,content_settings_2ff42bfc8f6c41c0bb8359a8006de4d0,content_editSettings_2ff42bfc8f6c41c0bb8359a8006de4d0,content_edit_2ff42bfc8f6c41c0bb8359a8006de4d0,properties_folder_2ff42bfc8f6c41c0bb8359a8006de4d0,itemcarot_managerecord_2ff42bfc8f6c41c0bb8359a8006de4d0,comments_tool_2ff42bfc8f6c41c0bb8359a8006de4d0,subscriptions_list_2ff42bfc8f6c41c0bb8359a8006de4d0,content_readfile_2ff42bfc8f6c41c0bb8359a8006de4d0,content_overwrite_2ff42bfc8f6c41c0bb8359a8006de4d0,passes_tool_2ff42bfc8f6c41c0bb8359a8006de4d0,permissions_tool_2ff42bfc8f6c41c0bb8359a8006de4d0,content_add_alignment_2ff42bfc8f6c41c0bb8359a8006de4d0,content_tracking_2ff42bfc8f6c41c0bb8359a8006de4d0,content_versions_2ff42bfc8f6c41c0bb8359a8006de4d0,*separator*,*separator*,bookmarkId_2ff42bfc8f6c41c0bb8359a8006de4d0,itemsId_2ff42bfc8f6c41c0bb8359a8006de4d0,packagesId_2ff42bfc8f6c41c0bb8359a8006de4d0,emailId_2ff42bfc8f6c41c0bb8359a8006de4d0,removeContentFolderId_2ff42bfc8f6c41c0bb8359a8006de4d0,*separator*,copyContentId_2ff42bfc8f6c41c0bb8359a8006de4d0,moveContentId_2ff42bfc8f6c41c0bb8359a8006de4d0,*separator*,removeContentId_2ff42bfc8f6c41c0bb8359a8006de4d0,*separator*,Metadata_General_2ff42bfc8f6c41c0bb8359a8006de4d0,Metadata_Dublin_Core_2ff42bfc8f6c41c0bb8359a8006de4d0,Metadata_IMS_2ff42bfc8f6c41c0bb8359a8006de4d0,Metadata_Full_IMS_2ff42bfc8f6c41c0bb8359a8006de4d0,\" 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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('2ff42bfc8f6c41c0bb8359a8006de4d0');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span 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class=\"moduleSample\">\n </div>\n",
        "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_207703_1&content_id=_8023392_1&mode=view",
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data-ally-scoreindicator=\"_90880950_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880950_2/xid-90880950_2\" target=\"_blank\" rel=\"noreferrer noopener\">07C_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07C_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00iz&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880950_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_c2b3ac64670d4b3aba204adcc38b5ab4\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_c2b3ac64670d4b3aba204adcc38b5ab4',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_c2b3ac64670d4b3aba204adcc38b5ab4',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_c2b3ac64670d4b3aba204adcc38b5ab4',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"90880950_2_fileReadWritePermAvl\" id=\"90880950_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('c2b3ac64670d4b3aba204adcc38b5ab4');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880951_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880951_2/xid-90880951_2\" target=\"_blank\" rel=\"noreferrer noopener\">07D_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07D_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j1&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880951_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_cadc939cddfc4280b060bfac42c30e08,open_with_browser_cadc939cddfc4280b060bfac42c30e08,open_with_bbdrive_cadc939cddfc4280b060bfac42c30e08,openWebId_cadc939cddfc4280b060bfac42c30e08,view360Id_cadc939cddfc4280b060bfac42c30e08,*separator*,*separator*,ax-ally-placeholder_cadc939cddfc4280b060bfac42c30e08,ax-ally-markForAxAnalysis_cadc939cddfc4280b060bfac42c30e08,*separator*,*separator*,content_settings_cadc939cddfc4280b060bfac42c30e08,content_editSettings_cadc939cddfc4280b060bfac42c30e08,content_edit_cadc939cddfc4280b060bfac42c30e08,properties_folder_cadc939cddfc4280b060bfac42c30e08,itemcarot_managerecord_cadc939cddfc4280b060bfac42c30e08,comments_tool_cadc939cddfc4280b060bfac42c30e08,subscriptions_list_cadc939cddfc4280b060bfac42c30e08,content_readfile_cadc939cddfc4280b060bfac42c30e08,content_overwrite_cadc939cddfc4280b060bfac42c30e08,passes_tool_cadc939cddfc4280b060bfac42c30e08,permissions_tool_cadc939cddfc4280b060bfac42c30e08,content_add_alignment_cadc939cddfc4280b060bfac42c30e08,content_tracking_cadc939cddfc4280b060bfac42c30e08,content_versions_cadc939cddfc4280b060bfac42c30e08,*separator*,*separator*,bookmarkId_cadc939cddfc4280b060bfac42c30e08,itemsId_cadc939cddfc4280b060bfac42c30e08,packagesId_cadc939cddfc4280b060bfac42c30e08,emailId_cadc939cddfc4280b060bfac42c30e08,removeContentFolderId_cadc939cddfc4280b060bfac42c30e08,*separator*,copyContentId_cadc939cddfc4280b060bfac42c30e08,moveContentId_cadc939cddfc4280b060bfac42c30e08,*separator*,removeContentId_cadc939cddfc4280b060bfac42c30e08,*separator*,Metadata_General_cadc939cddfc4280b060bfac42c30e08,Metadata_Dublin_Core_cadc939cddfc4280b060bfac42c30e08,Metadata_IMS_cadc939cddfc4280b060bfac42c30e08,Metadata_Full_IMS_cadc939cddfc4280b060bfac42c30e08,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_cadc939cddfc4280b060bfac42c30e08\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"90880951_2_fileReadWritePermAvl\" id=\"90880951_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('cadc939cddfc4280b060bfac42c30e08');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880952_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880952_2/xid-90880952_2\" target=\"_blank\" rel=\"noreferrer noopener\">07E_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j3&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880952_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_2717c401524546a18def931e58dd7fd0,open_with_browser_2717c401524546a18def931e58dd7fd0,open_with_bbdrive_2717c401524546a18def931e58dd7fd0,openWebId_2717c401524546a18def931e58dd7fd0,view360Id_2717c401524546a18def931e58dd7fd0,*separator*,*separator*,ax-ally-placeholder_2717c401524546a18def931e58dd7fd0,ax-ally-markForAxAnalysis_2717c401524546a18def931e58dd7fd0,*separator*,*separator*,content_settings_2717c401524546a18def931e58dd7fd0,content_editSettings_2717c401524546a18def931e58dd7fd0,content_edit_2717c401524546a18def931e58dd7fd0,properties_folder_2717c401524546a18def931e58dd7fd0,itemcarot_managerecord_2717c401524546a18def931e58dd7fd0,comments_tool_2717c401524546a18def931e58dd7fd0,subscriptions_list_2717c401524546a18def931e58dd7fd0,content_readfile_2717c401524546a18def931e58dd7fd0,content_overwrite_2717c401524546a18def931e58dd7fd0,passes_tool_2717c401524546a18def931e58dd7fd0,permissions_tool_2717c401524546a18def931e58dd7fd0,content_add_alignment_2717c401524546a18def931e58dd7fd0,content_tracking_2717c401524546a18def931e58dd7fd0,content_versions_2717c401524546a18def931e58dd7fd0,*separator*,*separator*,bookmarkId_2717c401524546a18def931e58dd7fd0,itemsId_2717c401524546a18def931e58dd7fd0,packagesId_2717c401524546a18def931e58dd7fd0,emailId_2717c401524546a18def931e58dd7fd0,removeContentFolderId_2717c401524546a18def931e58dd7fd0,*separator*,copyContentId_2717c401524546a18def931e58dd7fd0,moveContentId_2717c401524546a18def931e58dd7fd0,*separator*,removeContentId_2717c401524546a18def931e58dd7fd0,*separator*,Metadata_General_2717c401524546a18def931e58dd7fd0,Metadata_Dublin_Core_2717c401524546a18def931e58dd7fd0,Metadata_IMS_2717c401524546a18def931e58dd7fd0,Metadata_Full_IMS_2717c401524546a18def931e58dd7fd0,\" 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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('2717c401524546a18def931e58dd7fd0');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880953_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880953_2/xid-90880953_2\" target=\"_blank\" rel=\"noreferrer noopener\">07F_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07F_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j5&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880953_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_c28d154f3f244322a3bec16e2f784dde,open_with_browser_c28d154f3f244322a3bec16e2f784dde,open_with_bbdrive_c28d154f3f244322a3bec16e2f784dde,openWebId_c28d154f3f244322a3bec16e2f784dde,view360Id_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,ax-ally-placeholder_c28d154f3f244322a3bec16e2f784dde,ax-ally-markForAxAnalysis_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,content_settings_c28d154f3f244322a3bec16e2f784dde,content_editSettings_c28d154f3f244322a3bec16e2f784dde,content_edit_c28d154f3f244322a3bec16e2f784dde,properties_folder_c28d154f3f244322a3bec16e2f784dde,itemcarot_managerecord_c28d154f3f244322a3bec16e2f784dde,comments_tool_c28d154f3f244322a3bec16e2f784dde,subscriptions_list_c28d154f3f244322a3bec16e2f784dde,content_readfile_c28d154f3f244322a3bec16e2f784dde,content_overwrite_c28d154f3f244322a3bec16e2f784dde,passes_tool_c28d154f3f244322a3bec16e2f784dde,permissions_tool_c28d154f3f244322a3bec16e2f784dde,content_add_alignment_c28d154f3f244322a3bec16e2f784dde,content_tracking_c28d154f3f244322a3bec16e2f784dde,content_versions_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,bookmarkId_c28d154f3f244322a3bec16e2f784dde,itemsId_c28d154f3f244322a3bec16e2f784dde,packagesId_c28d154f3f244322a3bec16e2f784dde,emailId_c28d154f3f244322a3bec16e2f784dde,removeContentFolderId_c28d154f3f244322a3bec16e2f784dde,*separator*,copyContentId_c28d154f3f244322a3bec16e2f784dde,moveContentId_c28d154f3f244322a3bec16e2f784dde,*separator*,removeContentId_c28d154f3f244322a3bec16e2f784dde,*separator*,Metadata_General_c28d154f3f244322a3bec16e2f784dde,Metadata_Dublin_Core_c28d154f3f244322a3bec16e2f784dde,Metadata_IMS_c28d154f3f244322a3bec16e2f784dde,Metadata_Full_IMS_c28d154f3f244322a3bec16e2f784dde,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_c28d154f3f244322a3bec16e2f784dde\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_c28d154f3f244322a3bec16e2f784dde',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_c28d154f3f244322a3bec16e2f784dde',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_c28d154f3f244322a3bec16e2f784dde',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"90880953_2_fileReadWritePermAvl\" id=\"90880953_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('c28d154f3f244322a3bec16e2f784dde');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_90880943_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880943_2/xid-90880943_2\" target=\"_blank\" rel=\"noreferrer noopener\">07G_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07G_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j7&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880943_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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bb:menuorder=\"openId_81aaded9846641a9ba6a2b547c387a5a,open_with_browser_81aaded9846641a9ba6a2b547c387a5a,open_with_bbdrive_81aaded9846641a9ba6a2b547c387a5a,openWebId_81aaded9846641a9ba6a2b547c387a5a,view360Id_81aaded9846641a9ba6a2b547c387a5a,*separator*,*separator*,ax-ally-placeholder_81aaded9846641a9ba6a2b547c387a5a,ax-ally-markForAxAnalysis_81aaded9846641a9ba6a2b547c387a5a,*separator*,*separator*,content_settings_81aaded9846641a9ba6a2b547c387a5a,content_editSettings_81aaded9846641a9ba6a2b547c387a5a,content_edit_81aaded9846641a9ba6a2b547c387a5a,properties_folder_81aaded9846641a9ba6a2b547c387a5a,itemcarot_managerecord_81aaded9846641a9ba6a2b547c387a5a,comments_tool_81aaded9846641a9ba6a2b547c387a5a,subscriptions_list_81aaded9846641a9ba6a2b547c387a5a,content_readfile_81aaded9846641a9ba6a2b547c387a5a,content_overwrite_81aaded9846641a9ba6a2b547c387a5a,passes_tool_81aaded9846641a9ba6a2b547c387a5a,permissions_tool_81aaded9846641a9ba6a2b547c387a5a,content_add_alignment_81aaded9846641a9ba6a2b547c387a5a,content_tracking_81aaded9846641a9ba6a2b547c387a5a,content_versions_81aaded9846641a9ba6a2b547c387a5a,*separator*,*separator*,bookmarkId_81aaded9846641a9ba6a2b547c387a5a,itemsId_81aaded9846641a9ba6a2b547c387a5a,packagesId_81aaded9846641a9ba6a2b547c387a5a,emailId_81aaded9846641a9ba6a2b547c387a5a,removeContentFolderId_81aaded9846641a9ba6a2b547c387a5a,*separator*,copyContentId_81aaded9846641a9ba6a2b547c387a5a,moveContentId_81aaded9846641a9ba6a2b547c387a5a,*separator*,removeContentId_81aaded9846641a9ba6a2b547c387a5a,*separator*,Metadata_General_81aaded9846641a9ba6a2b547c387a5a,Metadata_Dublin_Core_81aaded9846641a9ba6a2b547c387a5a,Metadata_IMS_81aaded9846641a9ba6a2b547c387a5a,Metadata_Full_IMS_81aaded9846641a9ba6a2b547c387a5a,\" 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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('81aaded9846641a9ba6a2b547c387a5a');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n</div>\n  </div>\n\n <div id=\"_8023392_1previewModule\" class=\"moduleSample\">\n </div>\n",
    "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_207703_1&content_id=_8023392_1&mode=view",
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        "title": "Video Lectures",
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bb:menuorder=\"openId_a39bbef8f73443d383c6ca6fc8a4396c,open_with_browser_a39bbef8f73443d383c6ca6fc8a4396c,open_with_bbdrive_a39bbef8f73443d383c6ca6fc8a4396c,openWebId_a39bbef8f73443d383c6ca6fc8a4396c,view360Id_a39bbef8f73443d383c6ca6fc8a4396c,*separator*,*separator*,ax-ally-placeholder_a39bbef8f73443d383c6ca6fc8a4396c,ax-ally-markForAxAnalysis_a39bbef8f73443d383c6ca6fc8a4396c,*separator*,*separator*,content_settings_a39bbef8f73443d383c6ca6fc8a4396c,content_editSettings_a39bbef8f73443d383c6ca6fc8a4396c,content_edit_a39bbef8f73443d383c6ca6fc8a4396c,properties_folder_a39bbef8f73443d383c6ca6fc8a4396c,itemcarot_managerecord_a39bbef8f73443d383c6ca6fc8a4396c,comments_tool_a39bbef8f73443d383c6ca6fc8a4396c,subscriptions_list_a39bbef8f73443d383c6ca6fc8a4396c,content_readfile_a39bbef8f73443d383c6ca6fc8a4396c,content_overwrite_a39bbef8f73443d383c6ca6fc8a4396c,passes_tool_a39bbef8f73443d383c6ca6fc8a4396c,permissions_tool_a39bbef8f73443d383c6ca6fc8a4396c,content_add_alignment_a39bbef8f73443d383c6ca6fc8a4396c,content_tracking_a39bbef8f73443d383c6ca6fc8a4396c,content_versions_a39bbef8f73443d383c6ca6fc8a4396c,*separator*,*separator*,bookmarkId_a39bbef8f73443d383c6ca6fc8a4396c,itemsId_a39bbef8f73443d383c6ca6fc8a4396c,packagesId_a39bbef8f73443d383c6ca6fc8a4396c,emailId_a39bbef8f73443d383c6ca6fc8a4396c,removeContentFolderId_a39bbef8f73443d383c6ca6fc8a4396c,*separator*,copyContentId_a39bbef8f73443d383c6ca6fc8a4396c,moveContentId_a39bbef8f73443d383c6ca6fc8a4396c,*separator*,removeContentId_a39bbef8f73443d383c6ca6fc8a4396c,*separator*,Metadata_General_a39bbef8f73443d383c6ca6fc8a4396c,Metadata_Dublin_Core_a39bbef8f73443d383c6ca6fc8a4396c,Metadata_IMS_a39bbef8f73443d383c6ca6fc8a4396c,Metadata_Full_IMS_a39bbef8f73443d383c6ca6fc8a4396c,\" 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bb:menuorder=\"openId_1ea8af7cb3484879b59bced3bbb77955,open_with_browser_1ea8af7cb3484879b59bced3bbb77955,open_with_bbdrive_1ea8af7cb3484879b59bced3bbb77955,openWebId_1ea8af7cb3484879b59bced3bbb77955,view360Id_1ea8af7cb3484879b59bced3bbb77955,*separator*,*separator*,ax-ally-placeholder_1ea8af7cb3484879b59bced3bbb77955,ax-ally-markForAxAnalysis_1ea8af7cb3484879b59bced3bbb77955,*separator*,*separator*,content_settings_1ea8af7cb3484879b59bced3bbb77955,content_editSettings_1ea8af7cb3484879b59bced3bbb77955,content_edit_1ea8af7cb3484879b59bced3bbb77955,properties_folder_1ea8af7cb3484879b59bced3bbb77955,itemcarot_managerecord_1ea8af7cb3484879b59bced3bbb77955,comments_tool_1ea8af7cb3484879b59bced3bbb77955,subscriptions_list_1ea8af7cb3484879b59bced3bbb77955,content_readfile_1ea8af7cb3484879b59bced3bbb77955,content_overwrite_1ea8af7cb3484879b59bced3bbb77955,passes_tool_1ea8af7cb3484879b59bced3bbb77955,permissions_tool_1ea8af7cb3484879b59bced3bbb77955,content_add_alignment_1ea8af7cb3484879b59bced3bbb77955,content_tracking_1ea8af7cb3484879b59bced3bbb77955,content_versions_1ea8af7cb3484879b59bced3bbb77955,*separator*,*separator*,bookmarkId_1ea8af7cb3484879b59bced3bbb77955,itemsId_1ea8af7cb3484879b59bced3bbb77955,packagesId_1ea8af7cb3484879b59bced3bbb77955,emailId_1ea8af7cb3484879b59bced3bbb77955,removeContentFolderId_1ea8af7cb3484879b59bced3bbb77955,*separator*,copyContentId_1ea8af7cb3484879b59bced3bbb77955,moveContentId_1ea8af7cb3484879b59bced3bbb77955,*separator*,removeContentId_1ea8af7cb3484879b59bced3bbb77955,*separator*,Metadata_General_1ea8af7cb3484879b59bced3bbb77955,Metadata_Dublin_Core_1ea8af7cb3484879b59bced3bbb77955,Metadata_IMS_1ea8af7cb3484879b59bced3bbb77955,Metadata_Full_IMS_1ea8af7cb3484879b59bced3bbb77955,\" 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bb:menuorder=\"openId_c2b3ac64670d4b3aba204adcc38b5ab4,open_with_browser_c2b3ac64670d4b3aba204adcc38b5ab4,open_with_bbdrive_c2b3ac64670d4b3aba204adcc38b5ab4,openWebId_c2b3ac64670d4b3aba204adcc38b5ab4,view360Id_c2b3ac64670d4b3aba204adcc38b5ab4,*separator*,*separator*,ax-ally-placeholder_c2b3ac64670d4b3aba204adcc38b5ab4,ax-ally-markForAxAnalysis_c2b3ac64670d4b3aba204adcc38b5ab4,*separator*,*separator*,content_settings_c2b3ac64670d4b3aba204adcc38b5ab4,content_editSettings_c2b3ac64670d4b3aba204adcc38b5ab4,content_edit_c2b3ac64670d4b3aba204adcc38b5ab4,properties_folder_c2b3ac64670d4b3aba204adcc38b5ab4,itemcarot_managerecord_c2b3ac64670d4b3aba204adcc38b5ab4,comments_tool_c2b3ac64670d4b3aba204adcc38b5ab4,subscriptions_list_c2b3ac64670d4b3aba204adcc38b5ab4,content_readfile_c2b3ac64670d4b3aba204adcc38b5ab4,content_overwrite_c2b3ac64670d4b3aba204adcc38b5ab4,passes_tool_c2b3ac64670d4b3aba204adcc38b5ab4,permissions_tool_c2b3ac64670d4b3aba204adcc38b5ab4,content_add_alignment_c2b3ac64670d4b3aba204adcc38b5ab4,content_tracking_c2b3ac64670d4b3aba204adcc38b5ab4,content_versions_c2b3ac64670d4b3aba204adcc38b5ab4,*separator*,*separator*,bookmarkId_c2b3ac64670d4b3aba204adcc38b5ab4,itemsId_c2b3ac64670d4b3aba204adcc38b5ab4,packagesId_c2b3ac64670d4b3aba204adcc38b5ab4,emailId_c2b3ac64670d4b3aba204adcc38b5ab4,removeContentFolderId_c2b3ac64670d4b3aba204adcc38b5ab4,*separator*,copyContentId_c2b3ac64670d4b3aba204adcc38b5ab4,moveContentId_c2b3ac64670d4b3aba204adcc38b5ab4,*separator*,removeContentId_c2b3ac64670d4b3aba204adcc38b5ab4,*separator*,Metadata_General_c2b3ac64670d4b3aba204adcc38b5ab4,Metadata_Dublin_Core_c2b3ac64670d4b3aba204adcc38b5ab4,Metadata_IMS_c2b3ac64670d4b3aba204adcc38b5ab4,Metadata_Full_IMS_c2b3ac64670d4b3aba204adcc38b5ab4,\" 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bb:menuorder=\"openId_cadc939cddfc4280b060bfac42c30e08,open_with_browser_cadc939cddfc4280b060bfac42c30e08,open_with_bbdrive_cadc939cddfc4280b060bfac42c30e08,openWebId_cadc939cddfc4280b060bfac42c30e08,view360Id_cadc939cddfc4280b060bfac42c30e08,*separator*,*separator*,ax-ally-placeholder_cadc939cddfc4280b060bfac42c30e08,ax-ally-markForAxAnalysis_cadc939cddfc4280b060bfac42c30e08,*separator*,*separator*,content_settings_cadc939cddfc4280b060bfac42c30e08,content_editSettings_cadc939cddfc4280b060bfac42c30e08,content_edit_cadc939cddfc4280b060bfac42c30e08,properties_folder_cadc939cddfc4280b060bfac42c30e08,itemcarot_managerecord_cadc939cddfc4280b060bfac42c30e08,comments_tool_cadc939cddfc4280b060bfac42c30e08,subscriptions_list_cadc939cddfc4280b060bfac42c30e08,content_readfile_cadc939cddfc4280b060bfac42c30e08,content_overwrite_cadc939cddfc4280b060bfac42c30e08,passes_tool_cadc939cddfc4280b060bfac42c30e08,permissions_tool_cadc939cddfc4280b060bfac42c30e08,content_add_alignment_cadc939cddfc4280b060bfac42c30e08,content_tracking_cadc939cddfc4280b060bfac42c30e08,content_versions_cadc939cddfc4280b060bfac42c30e08,*separator*,*separator*,bookmarkId_cadc939cddfc4280b060bfac42c30e08,itemsId_cadc939cddfc4280b060bfac42c30e08,packagesId_cadc939cddfc4280b060bfac42c30e08,emailId_cadc939cddfc4280b060bfac42c30e08,removeContentFolderId_cadc939cddfc4280b060bfac42c30e08,*separator*,copyContentId_cadc939cddfc4280b060bfac42c30e08,moveContentId_cadc939cddfc4280b060bfac42c30e08,*separator*,removeContentId_cadc939cddfc4280b060bfac42c30e08,*separator*,Metadata_General_cadc939cddfc4280b060bfac42c30e08,Metadata_Dublin_Core_cadc939cddfc4280b060bfac42c30e08,Metadata_IMS_cadc939cddfc4280b060bfac42c30e08,Metadata_Full_IMS_cadc939cddfc4280b060bfac42c30e08,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_cadc939cddfc4280b060bfac42c30e08\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_cadc939cddfc4280b060bfac42c30e08',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <p>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8023392-dt-content-rid-90880952_2/xid-90880952_2\" target=\"_blank\" rel=\"noreferrer noopener\">07E_Slides</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module07/07E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00j3&amp;course_id=_207703_1&amp;ctxMenuXythosId=90880952_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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bb:menuorder=\"openId_c28d154f3f244322a3bec16e2f784dde,open_with_browser_c28d154f3f244322a3bec16e2f784dde,open_with_bbdrive_c28d154f3f244322a3bec16e2f784dde,openWebId_c28d154f3f244322a3bec16e2f784dde,view360Id_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,ax-ally-placeholder_c28d154f3f244322a3bec16e2f784dde,ax-ally-markForAxAnalysis_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,content_settings_c28d154f3f244322a3bec16e2f784dde,content_editSettings_c28d154f3f244322a3bec16e2f784dde,content_edit_c28d154f3f244322a3bec16e2f784dde,properties_folder_c28d154f3f244322a3bec16e2f784dde,itemcarot_managerecord_c28d154f3f244322a3bec16e2f784dde,comments_tool_c28d154f3f244322a3bec16e2f784dde,subscriptions_list_c28d154f3f244322a3bec16e2f784dde,content_readfile_c28d154f3f244322a3bec16e2f784dde,content_overwrite_c28d154f3f244322a3bec16e2f784dde,passes_tool_c28d154f3f244322a3bec16e2f784dde,permissions_tool_c28d154f3f244322a3bec16e2f784dde,content_add_alignment_c28d154f3f244322a3bec16e2f784dde,content_tracking_c28d154f3f244322a3bec16e2f784dde,content_versions_c28d154f3f244322a3bec16e2f784dde,*separator*,*separator*,bookmarkId_c28d154f3f244322a3bec16e2f784dde,itemsId_c28d154f3f244322a3bec16e2f784dde,packagesId_c28d154f3f244322a3bec16e2f784dde,emailId_c28d154f3f244322a3bec16e2f784dde,removeContentFolderId_c28d154f3f244322a3bec16e2f784dde,*separator*,copyContentId_c28d154f3f244322a3bec16e2f784dde,moveContentId_c28d154f3f244322a3bec16e2f784dde,*separator*,removeContentId_c28d154f3f244322a3bec16e2f784dde,*separator*,Metadata_General_c28d154f3f244322a3bec16e2f784dde,Metadata_Dublin_Core_c28d154f3f244322a3bec16e2f784dde,Metadata_IMS_c28d154f3f244322a3bec16e2f784dde,Metadata_Full_IMS_c28d154f3f244322a3bec16e2f784dde,\" 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file_9.pdf
./attachments/cell_261/file_9.pdf

Q&A

Cell description

Continue to ask questions and answer your classmates' questions in Piazza.

Participation in the class discussion is expected. It is unlikely you will go through the material without any questions. Please be sure to make at least one technically relevant posting, whether a question or comment.

To access Piazza, click Piazza Discussions on the course menu.

Technical 
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Assignment 7

Cell description

Assignment 7

has three problems. The first two are fairly straightforward applications of topics covered in the module, but rely significantly on topics in prior modules. The third problem expects that you extend the concepts discussed in this module in a new context; it involves viewing the Fourier series from the perspective of sampling theory. It is not necessarily more difficult or time consuming, but requires a more sophisticated approach.

The assignment is due by the end of Module 7, following the Assignment Guidelines.

To submit the assignment, click the Assignment 7 title above.

Technical 
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