{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":236,"title":"newRMS","description":"find root mean square of a signal x in less time than the test code and accurate to six places.","description_html":"\u003cp\u003efind root mean square of a signal x in less time than the test code and accurate to six places.\u003c/p\u003e","function_template":"function y = newRMS(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = rand(1,10^6);\r\ntic;\r\ny_new=round(newRMS(x)*10^6)/10^6;\r\nt_new=toc;\r\ntic;\r\ny_correct = round(sqrt(var(x,1)+mean(x)^2)*10^6)/10^6;\r\nt_correct=toc;\r\nassert(isequal(y_new,y_correct))\r\nassert(t_new\u003ct_correct)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":91,"test_suite_updated_at":"2012-02-02T15:53:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-02T15:53:23.000Z","updated_at":"2025-11-25T23:41:18.000Z","published_at":"2012-02-02T15:54:39.000Z","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\u003efind root mean square of a signal x in less time than the test code and accurate to six places.\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":2460,"title":"Signal Processing Basic - 1. 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Assume that the signal has been sampled at thousand times higher frequency than Nyquist frequency.\u003c/p\u003e\u003cp\u003eOutput signal may not match exactly with test suite and some tolerance is allowed (check the test suite). Output signal should be sampled at the instants where the input signal was sampled (implying same signal length as input).\u003c/p\u003e","function_template":"function y = stc(x,factor)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 1:10;\r\na = sin(2*pi*(50/500)*n);\r\nb = [0.5878    0.9458    0.9511    0.7323    0.2484   -0.3112   -0.7803   -0.9511   -0.9276   -0.5413];\r\nassert(sqrt(sum((b - stc(a,.9)).^2))\u003c.1)\r\n\r\n%%\r\na = [1 2 1 3 1 4 5];\r\nb = [1.0000    1.9900    1.1040    2.5680    1.7040    2.3125    4.5680];\r\nassert(sqrt(sum((b - stc(a,.9)).^2))\u003c.1);\r\n\r\n%%\r\nn = 1:10000;\r\na = sin(2*pi*(50/500)*n);\r\nb = a;\r\nassert(sqrt(sum((b - stc(a,1)).^2))\u003c.1);\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-23T11:47:33.000Z","updated_at":"2025-12-08T23:29:41.000Z","published_at":"2014-07-23T11:47:33.000Z","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\u003eInput vector V is a discrete time signal assuming the first sample is sampled at t=0. This signal has to be stretched in time.\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\u003eStretching factor (the second input) will be smaller than or equal to 1. Assume that the signal has been sampled at thousand times higher frequency than Nyquist frequency.\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\u003eOutput signal may not match exactly with test suite and some tolerance is allowed (check the test suite). 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Assume that the signal has been sampled at thousand times higher frequency than Nyquist frequency.\u003c/p\u003e\u003cp\u003eOutput signal may not match exactly with test suite and some tolerance is allowed (check the test suite). Output signal should be sampled at the instants where the input signal was sampled (implying same signal length as input).\u003c/p\u003e","function_template":"function y = stc(x,factor)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 1:10;\r\na = sin(2*pi*(50/500)*n);\r\nb = [0.5878    0.9458    0.9511    0.7323    0.2484   -0.3112   -0.7803   -0.9511   -0.9276   -0.5413];\r\nassert(sqrt(sum((b - stc(a,.9)).^2))\u003c.1)\r\n\r\n%%\r\na = [1 2 1 3 1 4 5];\r\nb = [1.0000    1.9900    1.1040    2.5680    1.7040    2.3125    4.5680];\r\nassert(sqrt(sum((b - stc(a,.9)).^2))\u003c.1);\r\n\r\n%%\r\nn = 1:10000;\r\na = sin(2*pi*(50/500)*n);\r\nb = a;\r\nassert(sqrt(sum((b - stc(a,1)).^2))\u003c.1);\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-23T11:47:33.000Z","updated_at":"2025-12-08T23:29:41.000Z","published_at":"2014-07-23T11:47:33.000Z","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\u003eInput vector V is a discrete time signal assuming the first sample is sampled at t=0. This signal has to be stretched in time.\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\u003eStretching factor (the second input) will be smaller than or equal to 1. Assume that the signal has been sampled at thousand times higher frequency than Nyquist frequency.\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\u003eOutput signal may not match exactly with test suite and some tolerance is allowed (check the test suite). 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