[amp_mcq option1=”|z| > 1″ option2=”|z| < 1\" option3=\"(Real part of z) > 0″ option4=”(Real part of z) < 0\" correct=\"option2\"]<\/p>\n
The correct answer is: B. |z| < 1<\/p>\n
The z-transform of a unit step function is given by:<\/p>\n
$U(z) = \\frac{1}{1-z^{-1}}$<\/p>\n
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 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| < 1. This is equivalent to |z| < 1.<\/p>\n
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
Option C is incorrect because the region of convergence does not include the line (Real part of z) > 0.<\/p>\n
Option D is incorrect because the region of convergence does not include the line (Real part of z) < 0.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”|z| > 1″ option2=”|z| < 1\" option3=\"(Real part of z) > 0″ option4=”(Real part of z) < 0\" correct=\"option2\"]\n<\/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-45785","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n