{"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>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a971d8a50ef0\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    Linear, stable and invertible                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    Non-linear, stable and non-invertible                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    Linear, stable and non-invertible                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    Linear, unstable and invertible                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--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 <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> be recovered from the input by multiplying the output by the inverse of the system function.<\/p>\n<ul>\n<li><strong>Option <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> 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>Join Our Telegram Channel Subscribe on YouTube<\/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":[],"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\" 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