Digital Signal Processing

Discrete Time Systems Described by Difference Equations

Question 1
Marks : +2 | -2
Pass Ratio : 100%
Zero-state response is also known as ____________
Free response
Forced response
Natural response
None of the mentioned
Explanation:
The zero-state response depends on the nature of the system and the input signal. Since this output is a response forced upon it by the input signal, it is also known as ‘Forced response’.
Question 2
Marks : +2 | -2
Pass Ratio : 100%
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)?
\\(\\frac{1}{1+a}\\) u(n)
\\(\\frac{1}{1-a}\\) u(n)
\\(\\frac{1}{1+a}\\)
\\(\\frac{1}{1-a}\\)
Explanation:
The assumed solution of the difference equation to the forcing equation x(n), called the particular solution of the difference equation is
Question 3
Marks : +2 | -2
Pass Ratio : 100%
The total solution of the difference equation is given as _______________
yp(n)-yh(n)
yp(n)+yh(n)
yh(n)-yp(n)
None of the mentioned
Explanation:
The linearity property of the linear constant coefficient difference equation allows us to add the homogeneous and particular solution in order to obtain the total solution.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
What is the particular solution of the difference equation y(n)=\\(\\frac{5}{6}y(n-1)-\\frac{1}{6}\\)y(n-2)+x(n) when the forcing function x(n)=2n, n≥0 and zero elsewhere?
\\(\\frac{1}{5}\\) 2n
\\(\\frac{5}{8}\\) 2n
\\(\\frac{8}{5}\\) 2n
\\(\\frac{5}{8}\\) 2-n
Explanation:
The assumed solution of the difference equation to the forcing equation x(n), called the particular solution of the difference equation is
Question 5
Marks : +2 | -2
Pass Ratio : 100%
If the system is initially relaxed at time n=0 and memory equals to zero, then the response of such state is called as ____________
Zero-state response
Zero-input response
Zero-condition response
None of the mentioned
Explanation:
The memory of the system, describes, in some case, the ‘state’ of the system, the output of the system is called as ‘zero-state response’.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
The solution obtained by assuming the input x(n) of the system is zero is ____________
General solution
Particular solution
Complete solution
Homogenous solution
Explanation:
By making the input x(n)=0 we will get a homogeneous difference equation and the solution of that difference equation is known as Homogenous or Complementary solution.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
What is the homogenous solution of the system described by the first order difference equation y(n)+ay(n-1)=x(n)?
c(a)n(where ‘c’ is a constant)
c(a)-n
c(-a)n
c(-a)-n
Explanation:
The assumed solution obtained by assigning x(n)=0 is
Question 8
Marks : +2 | -2
Pass Ratio : 100%
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)?
[-\\(\\frac{1}{5}\\) (-1)n–\\(\\frac{6}{5}\\) (4)n]u(n)
[\\(\\frac{1}{5}\\) (-1)n–\\(\\frac{6}{5}\\) (4)n]u(n)
[\\(\\frac{1}{5}\\) (-1)n+\\(\\frac{6}{5}\\) (4)n]u(n)
[-\\(\\frac{1}{5}\\) (-1)n+\\(\\frac{6}{5}\\) (4)n]u(n)
Explanation:
The homogenous solution of the given equation is yh(n)=C1(-1)n+C2(4)n—-(1)
Question 9
Marks : +2 | -2
Pass Ratio : 100%
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?
(-1)n-1 + (4)n-2
(-1)n+1 + (4)n+2
(-1)n+1 + (4)n-2
None of the mentioned
Explanation:
Given difference equation is y(n)-3y(n-1)-4y(n-2)=0—-(1)
Question 10
Marks : +2 | -2
Pass Ratio : 100%
Zero-input response is also known as Natural or Free response.
True
False
Explanation:
For a zero-input response, the input is zero and the output of the system is independent of the input of the system. So, the response if such system is also known as Natural or Free response.