{"id":44534,"date":"2024-04-15T21:45:06","date_gmt":"2024-04-15T21:45:06","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=44534"},"modified":"2024-04-15T21:45:06","modified_gmt":"2024-04-15T21:45:06","slug":"an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/","title":{"rendered":"An FIR system is described by the system function $$H\\left( z \\right) = 1 + \\frac{7}{2}{z^{ &#8211; 1}} + \\frac{3}{z}{z^{ &#8211; 2}}$$ 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_6a9700acae375\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    Maximum phase                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    Minimum phase                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    Mixed phase                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    Zero phase                <\/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>C. Mixed phase<\/strong><\/p>\n<p>An FIR system is a linear time-invariant (LTI) system with a finite impulse response (FIR). The system function of an FIR system is given by<\/p>\n<p>$$H(z) = \\sum_{n=0}^{N-1} h[n] z^{-n}$$<\/p>\n<p>where $h[n]$ is the impulse response of the system and $N$ is the number of taps in the impulse response.<\/p>\n<p>The phase of an FIR system is given by<\/p>\n<p>$$\\phi(e^{j\\omega}) = -\\sum_{n=0}^{N-1} n \\omega h[n]$$<\/p>\n<p>where $\\omega$ is the angular frequency.<\/p>\n<p>An FIR system is said to be minimum phase if its phase is minimum over all possible FIR systems with the same magnitude response. An FIR system is said to be maximum phase if <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\" <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> 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> its phase is maximum over all possible FIR systems with the same magnitude response. An FIR system is said to be mixed phase if its phase is neither minimum nor maximum.<\/p>\n<p>In this case, the system function is given by<\/p>\n<p>$$H(z) = 1 + \\frac{7}{2} z^{-1} + \\frac{3}{z} z^{-2}$$<\/p>\n<p>The phase of the system is given by<\/p>\n<p>$$\\phi(e^{j\\omega}) = -\\omega &#8211; \\frac{7}{2} \\sin(\\omega) &#8211; \\frac{3}{2} \\cos(\\omega)$$<\/p>\n<p>The phase of the system is not constant, so the system is not minimum phase or maximum phase. Therefore, the system is mixed phase.<\/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>An FIR system is described by the system function $$H\\left( z \\right) = 1 + \\frac{7}{2}{z^{ - 1}} + \\frac{3}{z}{z^{ - 2}}$$ 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\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An FIR system is described by the system function $$H\\left( z \\right) = 1 + \\frac{7}{2}{z^{ - 1}} + \\frac{3}{z}{z^{ - 2}}$$ The system is\" \/>\n<meta property=\"og:description\" content=\"Join Our Telegram Channel Subscribe on YouTube\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T21:45:06+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"An FIR system is described by the system function $$H\\left( z \\right) = 1 + \\frac{7}{2}{z^{ - 1}} + \\frac{3}{z}{z^{ - 2}}$$ The system is","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/","og_locale":"en_US","og_type":"article","og_title":"An FIR system is described by the system function $$H\\left( z \\right) = 1 + \\frac{7}{2}{z^{ - 1}} + \\frac{3}{z}{z^{ - 2}}$$ The system is","og_description":"Join Our Telegram Channel Subscribe on YouTube","og_url":"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T21:45:06+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/","url":"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/","name":"An FIR system is described by the system function $$H\\left( z \\right) = 1 + \\frac{7}{2}{z^{ - 1}} + \\frac{3}{z}{z^{ - 2}}$$ The system is","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T21:45:06+00:00","dateModified":"2024-04-15T21:45:06+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/an-fir-system-is-described-by-the-system-function-hleft-z-right-1-frac72z-1-frac3zz-2-the-system-is\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"Signal processing","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/signal-processing\/"},{"@type":"ListItem","position":3,"name":"An FIR system is described by the system function $$H\\left( z \\right) = 1 + \\frac{7}{2}{z^{ &#8211; 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