IT6502 Digital Signal Processing, Third year, Departmentof Electrical & Electronics Engineering, First and second Units Questions

PART A – (10 x 2 = 20 Marks)                    
1. What is Aliasing ?. How is it corrected ?.
2. Test the stability of the system y(n) = cosx(n) ?.  
3. Define even and odd signals ?.
  4. State and prove parseval’s theorem?.
5. Find the energy and power of x(n) = Aejωnu(n).  
6. What are the applications of FFT algorithm ?.
  7. Define Twiddle factor? .
8. Differentiate DIT-FFT & DIF-FFT algorithm ?.  
9. Write down DFT pair of equations.
10. Determine the number of multiplications required in the computation of 8-point DFT using
      FFT ?.    

                                              PART B-(5 x16=80 Marks)
11.a) (i) State & prove sampling theorem.                                                                                  (10)
         (ii) State & prove any two properties of z-transform.                                                         (6)
12.a) Determine the z-transform for the sequence.
           (i)  x (n) =  4ncos[  +   ] u(-n-1)                                                                               (4)
          (ii) x(n) = [-1/5]n u(n) + 5[1/2]-n u(-n-1)                                                                             (4)
          (iii) x(n) = u(n-2)                                                                                                                 (4)
         (iv) Find the inverse Z-transform of  X(Z) =  1/ ( 1−1.5 𝑍−1+ 0.5 𝑍−2) if ROC : |Z| > 1,      (4)


13.i) Check whether the following systems are Static or Dynamic, Linear or Non-linear, Time variant or invariant, Causal or non-causal, Stable or unstable.
                   (i)  y(n) = Cos[x(n)]                          ii) y(n) = x(-n+2)
                  (iii) y(n) = x(2n)                                iv) y(n) = x(n)Cosωn                                     (10)
          (ii) Convolve the sequence
                        i) x(n) = (  ) n  u(n) & h(n) = (   )n  u(n)                                                        (3)
                        ii) x1 (n) = {-1,2,3,4,5} &  x2(n) = { 6,7}                                                            (3)   
14. Find DFT of the sequence x(n) = {1,2,3,4,4,3,2,1} using radix-2 DIT-FFT & DIF-FFT 
         Algorithm.                                                                                                                         (16)  
   
15. (i) Compute the DFT of the four – point sequence x(n) = {0,1,2,3}.                                   (8)
        (ii) Find the IDFT of the sequence Y(k) = {1,0,1,0}.                                                         (8)