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₯
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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
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