Discrete Time System Analysis

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Analysis of Discrete time LTI Systems”.

1. Resolve the sequence  into a sum of weighted impulse sequences.
a) 2δ(n)+4δ(n-1)+3δ(n-3)
b) 2δ(n+1)+4δ(n)+3δ(n-2)
c) 2δ(n)+4δ(n-1)+3δ(n-2)
d) None of the mentioned

2. The formula y(n)=∑∞k=−∞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 ______________
a) Convolution sum
b) Convolution product
c) Convolution Difference
d) None of the mentioned

3. 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)?
Step-1:Folding
Step-2:Multiplication with x(k)
Step-3:Shifting
Step-4:Summation
a) 1-2-3-4
b) 1-2-4-3
c) 2-1-3-4
d) 1-3-2-4

4. 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}?
a) {1,3,6,3,1}
b) {1,2,3,2,1}
c) {1,3,6,5,3}
d) {1,1,1,0,0}

5. 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).
a) 1−an+11−a
b) 1−an−11−a
c) 1+an+11+a
d) None of the mentioned

6. x(n)*(h1(n)*h2(n))=(x(n)*h1(n))*h2(n).
a) True
b) False

7. Determine the impulse response for the cascade of two LTI systems having impulse responses h1(n)=(12)2 u(n) and h2(n)=(14)2 u(n).
a) (12)n[2−(12)n], n<0
b) (12)n[2−(12)n], n>0
c) (12)n[2+(12)n], n<0
d) (12)n[2+(12)n], n>0

For k<0, h1(n)= h2(n)=0 since the unit step function is defined only on the right hand side.
Therefore, h(k)=(12)k(14)n−k
=>h(n)=∑nk=0(12)k(14)n−k
=(14)n∑nk=0(2)k
=(14)n.(2n+1−1)
=(12)n[2−(12)n],n>0

8. x(n)*[h1(n)+h2(n)]=x(n)*h1(n)+x(n)*h2(n).
a) True
b) False

9. An LTI system is said to be causal if and only if?
a) Impulse response is non-zero for positive values of n
b) Impulse response is zero for positive values of n
c) Impulse response is non-zero for negative values of n
d) Impulse response is zero for negative values of n

10. x(n)*δ(n-n0)=?
a) x(n+n0)
b) x(n-n0)
c) x(-n-n0)
d) x(-n+n0)

11. Is the system with impulse response h(n)=2nu(n-1) stable.
a) True
b) False

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