{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2034,"title":"Finding fourier transform of a given vector","description":"Find the fourier transform of a given input vector \r\n\r\nfor ex a=[1 2 3 4]\r\n      \r\n       then y=[  10.0000 + 0.0000i  -2.0000 + 2.0000i  -2.0000 + 0.0000i  -2.0000 - 2.0000i]","description_html":"\u003cp\u003eFind the fourier transform of a given input vector\u003c/p\u003e\u003cp\u003efor ex a=[1 2 3 4]\u003c/p\u003e\u003cpre\u003e       then y=[  10.0000 + 0.0000i  -2.0000 + 2.0000i  -2.0000 + 0.0000i  -2.0000 - 2.0000i]\u003c/pre\u003e","function_template":"function y = fouriertrnsform(x)\r\n  y = fft(x);\r\nend","test_suite":"%%\r\nx = [1 2];\r\ny_correct =[3 -1];\r\nassert(isequal(fouriertrnsform(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":6728,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":141,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-05T17:07:59.000Z","updated_at":"2026-02-06T20:33:39.000Z","published_at":"2013-12-05T17:09:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the fourier transform of a given input vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor ex a=[1 2 3 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[       then y=[  10.0000 + 0.0000i  -2.0000 + 2.0000i  -2.0000 + 0.0000i  -2.0000 - 2.0000i]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2228,"title":"Time Expansion ","description":"How can you slow down any discrete-time signal?\r\n\r\nExample\r\n\r\nInput original signal x.\r\n\r\n x = [1 2 3 -1 -2 -5 -4] \r\n\r\nWe want to slow down n=3 times original signal. Output signal must be like y.\r\n\r\n y = [1 0 0 2 0 0 3 0 0 -1 0 0 -2 0 0 -5 0 0 -4]\r\n","description_html":"\u003cp\u003eHow can you slow down any discrete-time signal?\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eInput original signal x.\u003c/p\u003e\u003cpre\u003e x = [1 2 3 -1 -2 -5 -4] \u003c/pre\u003e\u003cp\u003eWe want to slow down n=3 times original signal. Output signal must be like y.\u003c/p\u003e\u003cpre\u003e y = [1 0 0 2 0 0 3 0 0 -1 0 0 -2 0 0 -5 0 0 -4]\u003c/pre\u003e","function_template":"function y= time_expansion(x,n)\r\ny=x;n;\r\nend","test_suite":"%%\r\nn=4\r\nx=[2 1 2 3 4 5 -3 4 -1 2 2 2]\r\ny_correct = [2 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 -3 0 0 0 4 0 0 0 -1 0 0 0 2 0 0 0 2 0 0 0 2];\r\nassert(isequal(time_expansion(x,n),y_correct))\r\n%%\r\nn=1\r\nx=[2 1 2 3 4 5 -3 4 -1 2 2 2]\r\ny_correct=x;\r\nassert(isequal(time_expansion(x,n),y_correct))\r\n%%\r\nn=5\r\nx=[2 1 2 3 4]\r\ny_correct=[2 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4];\r\nassert(isequal(time_expansion(x,n),y_correct))\r\n%%\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":22216,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":186,"test_suite_updated_at":"2014-03-02T12:59:19.000Z","rescore_all_solutions":false,"group_id":21,"created_at":"2014-03-02T12:48:45.000Z","updated_at":"2026-03-16T15:57:26.000Z","published_at":"2014-03-02T12:59:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHow can you slow down any discrete-time signal?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput original signal x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [1 2 3 -1 -2 -5 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe want to slow down n=3 times original signal. Output signal must be like y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [1 0 0 2 0 0 3 0 0 -1 0 0 -2 0 0 -5 0 0 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1460,"title":"Cosine frequency doubler","description":"Given an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.  ","description_html":"\u003cp\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.\u003c/p\u003e","function_template":"function y = SineDublr(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nt = 0:0.001:1;\r\nx = cos(2*pi*5*t);\r\ny_correct = cos(2*pi*10*t);\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.002:1;\r\nx = cos(2*pi*15*t)+2;\r\ny_correct = cos(2*pi*30*t)+2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nx = 3*cos(2*pi*35*t)-2;\r\ny_correct = 3*cos(2*pi*70*t)-2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nfreq = floor(rand*100);\r\noffset = floor(rand*10);\r\namp = floor(rand*10);\r\nx = amp*cos(2*pi*freq*t)-offset;\r\ny_correct = amp*cos(2*pi*2*freq*t)-offset;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13007,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2013-04-25T21:13:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-25T20:47:42.000Z","updated_at":"2026-01-20T14:22:54.000Z","published_at":"2013-04-25T20:47:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency. The output should have the same mean and amplitude as the input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":220,"title":"Signal filtering","description":"You are given a vector, containing a superposition of target signal and white gaussian noise. Return a vector, containing the estimated signal, assuming the following conditions:\r\nsignal-to-noise ratio is greater than 1;\r\nthe sampling rate is at least 100 times greater than the target signal bandwidth.\r\nThe correlation coefficient of the resulting signal and the initial signal should be at least 0.95.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 133.875px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 66.9375px; transform-origin: 408px 66.9375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a vector, containing a superposition of target signal and white gaussian noise. Return a vector, containing the estimated signal, assuming the following conditions:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esignal-to-noise ratio is greater than 1;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe sampling rate is at least 100 times greater than the target signal bandwidth.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe correlation coefficient of the resulting signal and the initial signal should be at least 0.95.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = filt(x)\r\n  y = x;\r\nend","test_suite":"%%\r\ny = sin(2*pi*(0:0.0001:0.9999)*100)' + randn(10000,1);\r\nz = filt(y);\r\nassert((sin(2*pi*(0:0.0001:0.9999)*100)*z/norm(sin(2*pi*(0:0.0001:0.9999)*100))/norm(z))\u003e0.95)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":530,"edited_by":3348724,"edited_at":"2025-12-29T19:04:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2025-12-29T19:03:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-01T20:49:35.000Z","updated_at":"2026-01-12T20:18:36.000Z","published_at":"2012-02-01T21:51:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a vector, containing a superposition of target signal and white gaussian noise. Return a vector, containing the estimated signal, assuming the following conditions:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esignal-to-noise ratio is greater than 1;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe sampling rate is at least 100 times greater than the target signal bandwidth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correlation coefficient of the resulting signal and the initial signal should be at least 0.95.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2607,"title":"Generate Square Wave","description":"Generate a square wave of desired length, number of complete cycles and duty cycle. Here, duty cycle is defined as the fraction of a complete cycle for which the cycle is at high value. Loops are not allowed.","description_html":"\u003cp\u003eGenerate a square wave of desired length, number of complete cycles and duty cycle. Here, duty cycle is defined as the fraction of a complete cycle for which the cycle is at high value. Loops are not allowed.\u003c/p\u003e","function_template":"function y = genSq(len,number_of_cycle,duty)\r\n\r\n\r\n  \r\nend","test_suite":"%%\r\nlen = 10;\r\nnum_cycle = 5;\r\nduty = 0.5;\r\ny_correct = [1 0 1 0 1 0 1 0 1 0];\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\nlen = 20;\r\nnum_cycle = 4;\r\nduty = .2;\r\ny_correct = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0];\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\nlen = 10;\r\nnum_cycle = 1;\r\nduty = 1;\r\ny_correct = ones(1,10);\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\nlen = 10;\r\nnum_cycle = 1;\r\nduty = 0;\r\ny_correct = zeros(1,10);\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\ntxt = fileread('genSq.m');\r\nassert(isempty(strfind(txt,'for')));\r\nassert(isempty(strfind(txt,'while')));\r\nassert(isempty(strfind(txt,'if')));","published":true,"deleted":false,"likes_count":7,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":261,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":29,"created_at":"2014-09-27T12:46:30.000Z","updated_at":"2026-04-01T09:51:59.000Z","published_at":"2014-09-27T12:46:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate a square wave of desired length, number of complete cycles and duty cycle. Here, duty cycle is defined as the fraction of a complete cycle for which the cycle is at high value. Loops are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2034,"title":"Finding fourier transform of a given vector","description":"Find the fourier transform of a given input vector \r\n\r\nfor ex a=[1 2 3 4]\r\n      \r\n       then y=[  10.0000 + 0.0000i  -2.0000 + 2.0000i  -2.0000 + 0.0000i  -2.0000 - 2.0000i]","description_html":"\u003cp\u003eFind the fourier transform of a given input vector\u003c/p\u003e\u003cp\u003efor ex a=[1 2 3 4]\u003c/p\u003e\u003cpre\u003e       then y=[  10.0000 + 0.0000i  -2.0000 + 2.0000i  -2.0000 + 0.0000i  -2.0000 - 2.0000i]\u003c/pre\u003e","function_template":"function y = fouriertrnsform(x)\r\n  y = fft(x);\r\nend","test_suite":"%%\r\nx = [1 2];\r\ny_correct =[3 -1];\r\nassert(isequal(fouriertrnsform(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":6728,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":141,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-12-05T17:07:59.000Z","updated_at":"2026-02-06T20:33:39.000Z","published_at":"2013-12-05T17:09:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the fourier transform of a given input vector\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor ex a=[1 2 3 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[       then y=[  10.0000 + 0.0000i  -2.0000 + 2.0000i  -2.0000 + 0.0000i  -2.0000 - 2.0000i]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2228,"title":"Time Expansion ","description":"How can you slow down any discrete-time signal?\r\n\r\nExample\r\n\r\nInput original signal x.\r\n\r\n x = [1 2 3 -1 -2 -5 -4] \r\n\r\nWe want to slow down n=3 times original signal. Output signal must be like y.\r\n\r\n y = [1 0 0 2 0 0 3 0 0 -1 0 0 -2 0 0 -5 0 0 -4]\r\n","description_html":"\u003cp\u003eHow can you slow down any discrete-time signal?\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eInput original signal x.\u003c/p\u003e\u003cpre\u003e x = [1 2 3 -1 -2 -5 -4] \u003c/pre\u003e\u003cp\u003eWe want to slow down n=3 times original signal. Output signal must be like y.\u003c/p\u003e\u003cpre\u003e y = [1 0 0 2 0 0 3 0 0 -1 0 0 -2 0 0 -5 0 0 -4]\u003c/pre\u003e","function_template":"function y= time_expansion(x,n)\r\ny=x;n;\r\nend","test_suite":"%%\r\nn=4\r\nx=[2 1 2 3 4 5 -3 4 -1 2 2 2]\r\ny_correct = [2 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 -3 0 0 0 4 0 0 0 -1 0 0 0 2 0 0 0 2 0 0 0 2];\r\nassert(isequal(time_expansion(x,n),y_correct))\r\n%%\r\nn=1\r\nx=[2 1 2 3 4 5 -3 4 -1 2 2 2]\r\ny_correct=x;\r\nassert(isequal(time_expansion(x,n),y_correct))\r\n%%\r\nn=5\r\nx=[2 1 2 3 4]\r\ny_correct=[2 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4];\r\nassert(isequal(time_expansion(x,n),y_correct))\r\n%%\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":22216,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":186,"test_suite_updated_at":"2014-03-02T12:59:19.000Z","rescore_all_solutions":false,"group_id":21,"created_at":"2014-03-02T12:48:45.000Z","updated_at":"2026-03-16T15:57:26.000Z","published_at":"2014-03-02T12:59:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHow can you slow down any discrete-time signal?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput original signal x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [1 2 3 -1 -2 -5 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe want to slow down n=3 times original signal. Output signal must be like y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [1 0 0 2 0 0 3 0 0 -1 0 0 -2 0 0 -5 0 0 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1460,"title":"Cosine frequency doubler","description":"Given an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.  ","description_html":"\u003cp\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.\u003c/p\u003e","function_template":"function y = SineDublr(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nt = 0:0.001:1;\r\nx = cos(2*pi*5*t);\r\ny_correct = cos(2*pi*10*t);\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.002:1;\r\nx = cos(2*pi*15*t)+2;\r\ny_correct = cos(2*pi*30*t)+2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nx = 3*cos(2*pi*35*t)-2;\r\ny_correct = 3*cos(2*pi*70*t)-2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nfreq = floor(rand*100);\r\noffset = floor(rand*10);\r\namp = floor(rand*10);\r\nx = amp*cos(2*pi*freq*t)-offset;\r\ny_correct = amp*cos(2*pi*2*freq*t)-offset;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13007,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2013-04-25T21:13:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-25T20:47:42.000Z","updated_at":"2026-01-20T14:22:54.000Z","published_at":"2013-04-25T20:47:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency. The output should have the same mean and amplitude as the input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":220,"title":"Signal filtering","description":"You are given a vector, containing a superposition of target signal and white gaussian noise. Return a vector, containing the estimated signal, assuming the following conditions:\r\nsignal-to-noise ratio is greater than 1;\r\nthe sampling rate is at least 100 times greater than the target signal bandwidth.\r\nThe correlation coefficient of the resulting signal and the initial signal should be at least 0.95.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 133.875px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 66.9375px; transform-origin: 408px 66.9375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a vector, containing a superposition of target signal and white gaussian noise. Return a vector, containing the estimated signal, assuming the following conditions:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esignal-to-noise ratio is greater than 1;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe sampling rate is at least 100 times greater than the target signal bandwidth.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe correlation coefficient of the resulting signal and the initial signal should be at least 0.95.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = filt(x)\r\n  y = x;\r\nend","test_suite":"%%\r\ny = sin(2*pi*(0:0.0001:0.9999)*100)' + randn(10000,1);\r\nz = filt(y);\r\nassert((sin(2*pi*(0:0.0001:0.9999)*100)*z/norm(sin(2*pi*(0:0.0001:0.9999)*100))/norm(z))\u003e0.95)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":530,"edited_by":3348724,"edited_at":"2025-12-29T19:04:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2025-12-29T19:03:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-01T20:49:35.000Z","updated_at":"2026-01-12T20:18:36.000Z","published_at":"2012-02-01T21:51:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a vector, containing a superposition of target signal and white gaussian noise. Return a vector, containing the estimated signal, assuming the following conditions:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esignal-to-noise ratio is greater than 1;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe sampling rate is at least 100 times greater than the target signal bandwidth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correlation coefficient of the resulting signal and the initial signal should be at least 0.95.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2607,"title":"Generate Square Wave","description":"Generate a square wave of desired length, number of complete cycles and duty cycle. Here, duty cycle is defined as the fraction of a complete cycle for which the cycle is at high value. Loops are not allowed.","description_html":"\u003cp\u003eGenerate a square wave of desired length, number of complete cycles and duty cycle. Here, duty cycle is defined as the fraction of a complete cycle for which the cycle is at high value. Loops are not allowed.\u003c/p\u003e","function_template":"function y = genSq(len,number_of_cycle,duty)\r\n\r\n\r\n  \r\nend","test_suite":"%%\r\nlen = 10;\r\nnum_cycle = 5;\r\nduty = 0.5;\r\ny_correct = [1 0 1 0 1 0 1 0 1 0];\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\nlen = 20;\r\nnum_cycle = 4;\r\nduty = .2;\r\ny_correct = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0];\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\nlen = 10;\r\nnum_cycle = 1;\r\nduty = 1;\r\ny_correct = ones(1,10);\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\nlen = 10;\r\nnum_cycle = 1;\r\nduty = 0;\r\ny_correct = zeros(1,10);\r\nassert(isequal(genSq(len,num_cycle,duty),y_correct))\r\n\r\n%%\r\ntxt = fileread('genSq.m');\r\nassert(isempty(strfind(txt,'for')));\r\nassert(isempty(strfind(txt,'while')));\r\nassert(isempty(strfind(txt,'if')));","published":true,"deleted":false,"likes_count":7,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":261,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":29,"created_at":"2014-09-27T12:46:30.000Z","updated_at":"2026-04-01T09:51:59.000Z","published_at":"2014-09-27T12:46:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate a square wave of desired length, number of complete cycles and duty cycle. Here, duty cycle is defined as the fraction of a complete cycle for which the cycle is at high value. Loops are not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"term":"tag:\"signal 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