{"id":154668,"date":"2023-08-07T10:09:56","date_gmt":"2023-08-07T04:39:56","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154668"},"modified":"2023-08-07T10:09:58","modified_gmt":"2023-08-07T04:39:58","slug":"the-symbols-%f0%9d%91%8e-and-%f0%9d%91%87-represent-positive-quantities-and-%f0%9d%91%a2%f0%9d%91%a1-is-the-unit-step-function-which-one-of-the-following-impulse-responses-is-not-the-output-of-a","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-symbols-%f0%9d%91%8e-and-%f0%9d%91%87-represent-positive-quantities-and-%f0%9d%91%a2%f0%9d%91%a1-is-the-unit-step-function-which-one-of-the-following-impulse-responses-is-not-the-output-of-a\/","title":{"rendered":"The symbols, \ud835\udc4e and \ud835\udc47, represent positive quantities, and \ud835\udc62(\ud835\udc61) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?"},"content":{"rendered":"\n<p>Q. The symbols, \ud835\udc4e and \ud835\udc47, represent positive quantities, and \ud835\udc62(\ud835\udc61) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?<\/p>\n\n\n\n<p>(A) \ud835\udc52<sup>+\ud835\udc4e\ud835\udc61<\/sup>\ud835\udc62(\ud835\udc61)<\/p>\n\n\n\n<p>(B) \ud835\udc52<sup>\u2212\ud835\udc4e(\ud835\udc61+\ud835\udc47)<\/sup>\ud835\udc62(\ud835\udc61)<\/p>\n\n\n\n<p>(C) 1 + \ud835\udc52<sup>\u2212\ud835\udc4e\ud835\udc61<\/sup>\ud835\udc62(\ud835\udc61)<\/p>\n\n\n\n<p>(D) \ud835\udc52<sup>\u2212\ud835\udc4e(\ud835\udc61\u2212\ud835\udc47)<\/sup>\ud835\udc62(\ud835\udc61)<\/p>\n\n\n\n<p>Ans: 1 + \ud835\udc52<sup>\u2212\ud835\udc4e\ud835\udc61<\/sup>\ud835\udc62(\ud835\udc61)<\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>a and T represents positive quantities.<br>u(t) is unit step function.<br>h(t)=1+e\u2212atu(t),\u00a0is non-causal<br>Here &#8216;1&#8217; is a constant and two sided so the system will be non-causal, because for causal system<br>h(t)=0,t&lt;0<br>\u22600,t>0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. The symbols, \ud835\udc4e and \ud835\udc47, represent positive quantities, and \ud835\udc62(\ud835\udc61) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system? (A) \ud835\udc52+\ud835\udc4e\ud835\udc61\ud835\udc62(\ud835\udc61) (B) \ud835\udc52\u2212\ud835\udc4e(\ud835\udc61+\ud835\udc47)\ud835\udc62(\ud835\udc61) (C) 1 + \ud835\udc52\u2212\ud835\udc4e\ud835\udc61\ud835\udc62(\ud835\udc61) (D) \ud835\udc52\u2212\ud835\udc4e(\ud835\udc61\u2212\ud835\udc47)\ud835\udc62(\ud835\udc61) Ans: 1 + \ud835\udc52\u2212\ud835\udc4e\ud835\udc61\ud835\udc62(\ud835\udc61) Solution: a and T represents positive quantities.u(t) is [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154669,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5141],"tags":[5140],"offerexpiration":[],"class_list":["post-154668","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154668","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154668"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154668\/revisions"}],"predecessor-version":[{"id":154670,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154668\/revisions\/154670"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154669"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154668"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/offerexpiration?post=154668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}