[amp_mcq option1=”h[n] is real for all n” option2=”h[n] is purely imaginary for all n” option3=”h[n] is real for only even n” option4=”h[n] is purely imaginary for only odd n” correct=”option1″]<\/p>\n
The correct answer is: A. h[n] is real for all n.<\/p>\n
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude that h[n] is real for all n.<\/p>\n
The impulse response of a causal and stable discrete-time system is the inverse Laplace transform of the system’s transfer function. The transfer function of a system with a zero at the origin has a pole at the origin with multiplicity 4. The inverse Laplace transform of a function with a pole at the origin with multiplicity 4 is a polynomial of degree 4 with real coefficients. Therefore, the impulse response of a causal and stable discrete-time system with a zero at the origin has multiplicity 4 is a real polynomial of degree 4.<\/p>\n
Since h[0] = 1, the constant term of the impulse response is 1. Therefore, the impulse response of a causal and stable discrete-time system with a zero at the origin has multiplicity 4 is a real polynomial of degree 4 with a constant term of 1. This means that h[n] is real for all n.<\/p>\n
Option B is incorrect because the impulse response of a causal and stable discrete-time system with a zero at the origin has multiplicity 4 is a real polynomial of degree 4, not a purely imaginary polynomial.<\/p>\n
Option C is incorrect because the impulse response of a causal and stable discrete-time system with a zero at the origin has multiplicity 4 is a real polynomial of degree 4, not a real polynomial for only even n.<\/p>\n
Option D is incorrect because the impulse response of a causal and stable discrete-time system with a zero at the origin has multiplicity 4 is a real polynomial of degree 4, not a purely imaginary polynomial for only odd n.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”h[n] is real for all n” option2=”h[n] is purely imaginary for all n” option3=”h[n] is real for only even n” option4=”h[n] is purely imaginary for only odd n” 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-53338","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n