MATH08013: A causal, linear, and time-invariant system is given by the following difference equation: Maths Assignment, UCC, Ireland
| University | University College Cork (UCC) |
| Subject | MATH08013: Maths Assignment |
Question 7
A causal, linear, and time–invariant system is given by the following difference equation:
π¦[π] = π¦[π β 1] + π¦[π + 2] + π₯[π β 1]
where π¦[0] = 1 and π¦[1] = 0.
i. Find the transfer function π»(π§) for this system.
ii. Plot the poles and zeros of π»(π§) and indicate the region of convergence (ROC).
iii. Find the unit sample response β[π] of this system.
Hint: Using the sample shifting property
β€{π₯[π β π]} = π§βππ(π§) ; π
ππΆ: π
ππΆπ₯
Stuck in Completing this Assignment and feeling stressed ? Take our Private Writing Services
Use the command zplane(b,a) in MATLAB for plotting poles and zeros where (b, a) are transfer function coefficients, specified as row vectors. The transfer function is defined in terms of π§β1:
π»(π§) = π΅(π§)
π΄(π§) = π(1) + π(2)π§β1 + π(3)π§β2 + β― + π(π + 1)π§βπ
π(1) + π(2)π§β1 + π(3)π§β2 + β― + π(π + 1)π§βπ
z = roots(b); % finding zeros from the roots of b
p = roots(a); % finding poles from the roots of a
Are You Searching Answer of this Question? Request Ireland Writers to Write a plagiarism Free Copy for You.
Looking for professional support to ace your courses? Our assignment expertsΒ Ireland are here to assist you every step of the way. Whether you need professional exam helpers or guidance on MATH08013 assignments like understanding causal, linear, and time-invariant systems, we've got you covered.
