{"id":47677,"date":"2024-04-15T22:30:12","date_gmt":"2024-04-15T22:30:12","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=47677"},"modified":"2024-04-15T22:30:12","modified_gmt":"2024-04-15T22:30:12","slug":"a-system-with-input-xn-and-output-yn-is-given-as-yleft-n-right-left-sin-5-over-6pi-n-rightxleft-n-right-the-system-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-system-with-input-xn-and-output-yn-is-given-as-yleft-n-right-left-sin-5-over-6pi-n-rightxleft-n-right-the-system-is\/","title":{"rendered":"A system with input x[n] and output y[n] is given as $$y\\left( n \\right) = \\left( {\\sin {5 \\over 6}\\pi n} \\right)x\\left( n \\right).$$ The system is"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;Linear, stable and invertible&#8221; option2=&#8221;Non-linear, stable and non-invertible&#8221; option3=&#8221;Linear, stable and non-invertible&#8221; option4=&#8221;Linear, unstable and invertible&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is: <strong>A. Linear, stable and invertible<\/strong><\/p>\n<p>A linear system is a system in which the output is a linear combination of the inputs. A stable system is a system that does not amplify the input signal. An invertible system is a system that can be inverted, i.e., the output can be recovered from the input.<\/p>\n<p>The given system is linear because the output is a linear combination of the inputs. The system is stable because the output does not grow without bound as the input increases. The system is invertible because the output can be recovered from the input by multiplying the output by the inverse of the system function.<\/p>\n<p>Here is a brief explanation of each option:<\/p>\n<ul>\n<li><strong>Option A: Linear, stable and invertible<\/strong><\/li>\n<\/ul>\n<p>This is the correct answer. The system is linear because the output is a linear combination of the inputs. The system is stable because the output does not grow without bound as the input increases. The system is invertible because the output can be recovered from the input by multiplying the output by the inverse of the system function.<\/p>\n<ul>\n<li><strong>Option B: Non-linear, stable and non-invertible<\/strong><\/li>\n<\/ul>\n<p>This option is incorrect. The system is linear because the output is a linear combination of the inputs. However, the system is not invertible because the output cannot be recovered from the input by multiplying the output by the inverse of the system function.<\/p>\n<ul>\n<li><strong>Option C: Linear, stable and non-invertible<\/strong><\/li>\n<\/ul>\n<p>This option is incorrect. The system is linear because the output is a linear combination of the inputs. However, the system is not stable because the output grows without bound as the input increases.<\/p>\n<ul>\n<li><strong>Option D: Linear, unstable and invertible<\/strong><\/li>\n<\/ul>\n<p>This option is incorrect. The system is linear because the output is a linear combination of the inputs. However, the system is not stable because the output grows without bound as the input increases.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;Linear, stable and invertible&#8221; option2=&#8221;Non-linear, stable and non-invertible&#8221; option3=&#8221;Linear, stable and non-invertible&#8221; option4=&#8221;Linear, unstable and invertible&#8221; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"class_list":["post-47677","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A system with input x[n] and output y[n] is given as $$y\\left( n \\right) = \\left( {\\sin {5 \\over 6}\\pi n} \\right)x\\left( n \\right).$$ The system is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-system-with-input-xn-and-output-yn-is-given-as-yleft-n-right-left-sin-5-over-6pi-n-rightxleft-n-right-the-system-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A system with input x[n] and output y[n] is given as $$y\\left( n \\right) = \\left( {\\sin {5 \\over 6}\\pi n} \\right)x\\left( n \\right).$$ The system is\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;Linear, stable and invertible&#8221; 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