{"id":45785,"date":"2024-04-15T22:02:58","date_gmt":"2024-04-15T22:02:58","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=45785"},"modified":"2024-04-15T22:02:58","modified_gmt":"2024-04-15T22:02:58","slug":"the-region-of-convergence-of-the-z-transform-of-a-unit-step-function-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-region-of-convergence-of-the-z-transform-of-a-unit-step-function-is\/","title":{"rendered":"The region of convergence of the z-transform of a unit step function is"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;|z| > 1&#8243; option2=&#8221;|z| < 1\" option3=\"(Real part of z) > 0&#8243; option4=&#8221;(Real part of z) < 0\" correct=\"option2\"]<!--more--><\/p>\n<p>The correct answer is: B. |z| &lt; 1<\/p>\n<p>The z-transform of a unit step function is <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> given by:<\/p>\n<p>$U(z) = \\frac{1}{1-z^{-1}}$<\/p>\n<p>The region of convergence of a z-transform is the set of all values of z for which the z-transform converges. The region of convergence of the z-transform of a unit step function is a circle with radius 1 and center at the origin. This is because the z-transform of a unit <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> step function is a geometric series with first term 1 and common ratio z-1. A geometric series converges if the absolute value of the common ratio is less than 1. In this case, the common ratio is z-1, so the z-transform converges if |z-1| &lt; 1. This is equivalent to |z| &lt; 1.<\/p>\n<p>Option A is incorrect because the region of convergence is a circle with radius 1, not a circle with radius greater than 1.<\/p>\n<p>Option C is incorrect because the region of convergence does not include the line (Real part of z) &gt; 0.<\/p>\n<p>Option D is incorrect because the region of convergence does not include the line (Real part of z) &lt; 0.<\/p>\n","protected":false},"excerpt":{"rendered":"[amp_mcq option1=&#8221;|z| > 1&#8243; option2=&#8221;|z| < 1\" option3=\"(Real part of z) > 0&#8243; Subscribe on YouTube option4=&#8221;(Real part of z) < 0\" correct=\"option2\"]\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>The region of convergence of the z-transform of a unit step function 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\/the-region-of-convergence-of-the-z-transform-of-a-unit-step-function-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The region of convergence of the z-transform of a unit step function is\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;|z| &gt; 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