[amp_mcq option1=”s + 3″ option2=”s – 2″ option3=”s – 6″ option4=”s + 1″ correct=”option1″]<\/p>\n
The correct answer is $\\boxed{s + 3}$.<\/p>\n
A causal system is a system that responds to an input only after the input has been applied. In other words, the output of a causal system cannot precede the input.<\/p>\n
The transfer function of a causal system must have no poles in the right half-plane. The transfer function of the given system, $H(s) = \\frac{1}{s^2 + s – 6}$, has a pole at $s = -3$. Therefore, the given system is not causal.<\/p>\n
To make the given system causal, we need to cascade it with another LTI system having a transfer function $H_1(s)$ such that the overall transfer function has no poles in the right half-plane.<\/p>\n
The transfer function $H_1(s) = s + 3$ has no poles in the right half-plane. Therefore, if we cascade the given system with a system having a transfer function of $s + 3$, the overall system will be causal.<\/p>\n
The other options, $s – 2$, $s – 6$, and $s + 1$, all have poles in the right half-plane. Therefore, if we cascade the given system with a system having any of these transfer functions, the overall system will not be causal.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”s + 3″ option2=”s – 2″ option3=”s – 6″ option4=”s + 1″ correct=”option1″]<\/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-57354","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n