# Discrete-Time Systems Difference Equations MCQ’s

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)=2^{n}, n≥0 and zero elsewhere?

a) 15 2^{n}

b) 58 2^{n}

c) 85 2^{n}

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) y_{p}(n)-y_{h}(n)

b) y_{p}(n)+y_{h}(n)

c) y_{h}(n)-y_{p}(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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