Digital Signal Processing Laboratory Viva Questions - Part 2

Q.1- Consider a causal system H(Z), H(Z)=1/H1(Z), where H1(Z) realizable (linear phase FIR filter), h1(n) ↔ H1(Z)
If we want stable system H(Z), then
(i) h1(n) is type-1 (h1(n) is odd length, symmetric)
(ii) h1(n) is type-2 (h1(n) is even length, symmetric)
(iii) h1(n) is type-3 (h1(n) is odd length, anti-symmetric)
(iv) h1(n) is type-4 (h1(n) is even length, anti-symmetric)

Which of them can be true?
(a) (i) or (ii)
(b) Only (i)
(c) (iii) or (iv)
(d) (i) or (iii)

Q.2- If x(n) is a sequence with alternate 1 and -1, If we passed the sequence through a filter h(n)↔H(), we will get an output sequence with all zeros. Then |H()| can be
(i) Monotonically increases from w=0 to w=π
(ii) Monotonically decreases from w=0 to w=π
(iii)Monotonically increases from w=0 to w=π/2, and monotonically decreases from w= π/2 to w=π
(iv)Monotonically decreases from w=0 to w=π/2, and monotonically increases from w= π/2 to w=π

Which of them can be true?
a) (i) and (iii)
b) (ii) and (iv)
c) (ii) only
d) (ii) and (iii)



Q.3- (i) DTFT exists means ROC contains |Z|=1
        (ii) ROC contains |Z|=1 means DTFT exists
        (iii) Stable system means ROC contains |Z|=1
        (iv) Causal system means ROC contains |Z|=1
   
     Which of them is always true?
(a) (i),(ii) and (iii)
(b) (i),(iii)
(c) (i),(iii) and (iv)
(d) (ii),(iii)
  Q.4- If A(Z) is the transfer function of stable all pass filter, then
             (i) A(Z)A() = 1
             (ii) |A(Z)| =1 for |Z|=1
            (iii) |A(Z)| >1 for |Z|<1
            (iv) |A(Z)| <1 for |Z|<1
             Which of them are true?
a) (ii) and (iii)
b) (ii) and (iv)
c) (i),(ii) and (iii)
d) (i),(ii) and (iv)
Q.5- If H(Z)=  is a causal system, And it is given that Hi(Z) is inverse system to H(Z), {h(n)* hi(n)=δ(n)}, Then what will be the ROC for Hi(Z)
          (i) |Z|<0.4
          (ii) |Z|>5
           (iii) 0.4<|Z|<5
True statements are:
a)  (ii) or (iii)
b) (i) or (iii)
c) (i) or (ii)
d) Anything


Q.6- (i) Linear phase FIR filter with constant group delay must have symmetric or anti-symmetric coefficient.
(ii) For Linear phase FIR, If Z0 is a zero of H(z), then 1/Z0 is also a zero of H(z).
(iii) If   > 0 for 0<w<  and   <0 for  <w<π , then  is band pass filter
True statements are:
(a) (i) only
(b) (ii) and (iii)
(c) (i) and (iii)
(d) (i), (ii) and (iii)

Q.7- The z-transform of a sequence x(n) is
      If the region of convergence includes the unit circle, find the DTFT of x(n) at w =  π/2.

(a)
(b)
(c)
(d) None of the above

Q.8- A sequence x(n) of length N1 = 100 is circularly convolved with a sequence h(n) of length N2 = 64 using DFTs of length N = 128. For what values of n will the circular convolution be equal to the linear convolution?

1) 100 ≤ n ≤ 128
2) 35 ≤n ≤ 127
3) 64 ≤ n ≤ 127
4) 100 ≤n ≤ 127


Q.9- The system function of an FIR filter is
                                        
    Find another causal FIR filter with h(n) = 0 for n > 4 that has the same frequency response magnitude.

(a)
(b)
(c)
(d) None of the above

Q.10- A linear shift-invariant system has a system function
                           
If H(z) is an all pass filter, what is the relationship between the numerator coefficients b(k)  and  the denominator coefficients a(k)?
a)  b(k) = a(p-k)  for k = 0,1,2,……p
b) b(k) = a(k-p)  for k = 0,1,2,……p
c) b(k) = a(k-p)  for k = 0,1,2,……p, and b(p) = 1
d) b(k) = a(p-k)  for k = 0,1,2,……p, and b(p) = 1



Ans. key:-
1) b
2) d
3) d
4) c
5) a
6) d
7) c
8) b
9) c
   10) d