ECE634 - Signals and Systems - Discrete Time System - Engineering Assignment Help

Assignment Task :

Instructions:(ECE634)

None of the usual in-class instructions apply except for one: do not collaborate or share exam solutions with anyone! Please don’t share a copy of the exam with anyone who has yet to download it – in other words, please respect the academic integrity of the exam process. This exam is administered in “open book, open notes, open internet” format, but do pay close attention to the timer that runs once you’ve opened the exam document on the Canvas quiz page. Please allow adequate time to scan/photograph your exam solutions and upload them as a single PDF document via the quiz submission link on the Canvas page BEFORE the timer runs out. I’ve appended some crib sheets to this exam in case you don’t have your textbook with you. Good luck!
 

Problem 1
A discrete-time system is described by the linear difference equation
y(n+1) - 0.6y(n) = x(n+1) – 2x(n)
(a) Write the characteristic equation for this system and find its roots.
(b) If y(-1) = -4 and the input x(n) = 0 for all n (i.e. zero-input case), write a mathematical expression for the system response y(n) for n greater than or equal to zero.
 

Problem 2
A 2nd order linear system is described by the equation below:
4y(n) – 4y(n-1) – 3y(n-2) = 4x(n-1)
(a) Write the characteristic equation for this system and find its roots.
(b) Write a mathematical expression for the unit impulse response h(n) of this system. Be sure to give numerical values for any undetermined coefficients.
(c) Is this system stable, marginally stable, or unstable? Please justify your response by reference to the locations of the roots of the characteristic equation you found in part (a).
 

Problem 3 (ECE634)
(a) The unit impulse response h(n) of a particular linear system is given by h(n) = (0.7)n+1 u(n). Write a closed-form mathematical expression for the response of this system to a unit step input x(n) = u(n) assuming that the system starts with zero state. [Hint: Table 3.1 of Lathi & Green is your friend!]
(b) Sketch approximately the step response.
(c) If the system is altered so that h(n) = (-0.7)n+1 u(n), how would this change the system response to the unit step input x(n) = u(n)? Be specific in your description of the changes you would observe, and feel free to use a sketch, similar to part (b), to illustrate the changes in the unit step response.

Problem 4
Given the discrete time signal x(n) shown below, please sketch the transformed versions of x(n) as indicated:
(a) y(n) = x(-2n + 1)
(b) y(n) = x(n+6)
(c) y(n) = x(n/2 – 1)

Problem 5
(a) Find the energy Ex and the average power Px for the signal x[n] depicted in Problem 4 above.
(b) Find the energy Ey for each of the transformed signals y[n] in parts (a), (b), and (c) of Problem 4 above

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