Discrete-Time Systems Difference Equations MCQ’s

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This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Discrete Time Systems Described by Difference Equations”.

1. What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?
a) (-1)n-1 + (4)n-2
b) (-1)n+1 + (4)n+2
c) (-1)n+1 + (4)n-2
d) None of the mentioned

2. The solution obtained by assuming the input x(n) of the system is zero is ____________
a) General solution
b) Particular solution
c) Complete solution
d) Homogenous solution

3. What is the particular solution of the difference equation y(n)=56𝑦(𝑛−1)−16y(n-2)+x(n) when the forcing function x(n)=2n, n≥0 and zero elsewhere?
a) 15 2n
b) 58 2n
c) 85 2n
d) 58 2-n

4. Zero-state response is also known as ____________
a) Free response
b) Forced response
c) Natural response
d) None of the mentioned

5. Zero-input response is also known as Natural or Free response.
a) True
b) False

6. The total solution of the difference equation is given as _______________
a) yp(n)-yh(n)
b) yp(n)+yh(n)
c) yh(n)-yp(n)
d) None of the mentioned

7. What is the homogenous solution of the system described by the first order difference equation y(n)+ay(n-1)=x(n)?
a) c(a)n(where ‘c’ is a constant)
b) c(a)-n
c) c(-a)n
d) c(-a)-n

8. What is the impulse response of the system described by the second order difference equation y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1)?
a) [-15 (-1)n–65 (4)n]u(n)
b) [15 (-1)n–65 (4)n]u(n)
c) [15 (-1)n+65 (4)n]u(n)
d) [-15 (-1)n+65 (4)n]u(n)

9. If the system is initially relaxed at time n=0 and memory equals to zero, then the response of such state is called as ____________
a) Zero-state response
b) Zero-input response
c) Zero-condition response
d) None of the mentioned

10. What is the particular solution of the first order difference equation y(n)+ay(n-1)=x(n) where |a|<1, when the input of the system x(n)=u(n)?
a) 11+𝑎 u(n)
b) 11−𝑎 u(n)
c) 11+𝑎
d) 11−𝑎

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