Digital Signal Processing

Analysis of Discrete time LTI Systems

Question 1
Marks : +2 | -2
Pass Ratio : 100%
x(n)*[h1(n)+h2(n)]=x(n)*h1(n)+x(n)*h2(n).
True
False
Explanation:
According to the properties of the convolution, convolution exhibits distributive property.
Question 2
Marks : +2 | -2
Pass Ratio : 100%
Resolve the sequence into a sum of weighted impulse sequences.
2δ(n)+4δ(n-1)+3δ(n-3)
2δ(n+1)+4δ(n)+3δ(n-2)
2δ(n)+4δ(n-1)+3δ(n-2)
None of the mentioned
Explanation:
We know that, x(n)δ(n-k)=x(k)δ(n-k)
Question 3
Marks : +2 | -2
Pass Ratio : 100%
Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=\\((\\frac{1}{2})^2\\) u(n) and h2(n)=\\((\\frac{1}{4})^2\\) u(n).
\\((\\frac{1}{2})^n[2-(\\frac{1}{2})^n]\\), n<0
\\((\\frac{1}{2})^n[2-(\\frac{1}{2})^n]\\), n>0
\\((\\frac{1}{2})^n[2+(\\frac{1}{2})^n]\\), n<0
\\((\\frac{1}{2})^n[2+(\\frac{1}{2})^n]\\), n>0
Explanation:
Let h2(n) be shifted and folded.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
x(n)*(h1(n)*h2(n))=(x(n)*h1(n))*h2(n).
True
False
Explanation:
According to the properties of convolution, Convolution of three signals obeys Associative property.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the order of the four operations that are needed to be done on h(k) in order to convolute x(k) and h(k)?
1-2-3-4
1-2-4-3
2-1-3-4
1-3-2-4
Explanation:
First the signal h(k) is folded to get h(-k). Then it is shifted by n to get h(n-k). Then it is multiplied by x(k) and then summed over -∞ to ∞.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
The formula y(n)=\\(\\sum_{k=-\\infty}^{\\infty}x(k)h(n-k)\\) that gives the response y(n) of the LTI system as the function of the input signal x(n) and the unit sample response h(n) is known as ______________
Convolution sum
Convolution product
Convolution Difference
None of the mentioned
Explanation:
The input x(n) is convoluted with the impulse response h(n) to yield the output y(n). As we are summing the different values, we call it as Convolution sum.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
Determine the output y(n) of a LTI system with impulse response h(n)=anu(n), |a|<1with the input sequence x(n)=u(n).
\\(\\frac{1-a^{n+1}}{1-a}\\)
\\(\\frac{1-a^{n-1}}{1-a}\\)
\\(\\frac{1+a^{n+1}}{1+a}\\)
None of the mentioned
Explanation:
Now fold the signal x(n) and shift it by one unit at a time and sum as follows
Question 8
Marks : +2 | -2
Pass Ratio : 100%
x(n)*δ(n-n0)=?
x(n+n0)
x(n-n0)
x(-n-n0)
x(-n+n0)
Explanation:
x(n)*δ(n-n0)=\\(\\sum_{k=-{\\infty}}^{\\infty} x(k)\\delta(n-k-n_0)\\)
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The impulse response of a LTI system is h(n)={1,1,1}. What is the response of the signal to the input x(n)={1,2,3}?
{1,3,6,3,1}
{1,2,3,2,1}
{1,3,6,5,3}
{1,1,1,0,0}
Explanation:
Let y(n)=x(n)*h(n)(‘*’ symbol indicates convolution symbol)
Question 10
Marks : +2 | -2
Pass Ratio : 100%
An LTI system is said to be causal if and only if?
Impulse response is non-zero for positive values of n
Impulse response is zero for positive values of n
Impulse response is non-zero for negative values of n
Impulse response is zero for negative values of n
Explanation:
Let us consider a LTI system having an output at time n=n0 given by the convolution formula