2011 Rajasthan Technical University B.Tech 5 Semester Computer science & engineering "Digital Signal Processing" question paper

Question Paper Details:


University: Rajasthan Technical University
Course: B.Tech Computer science & engineering 
Subject Digital Signal Processing
Exam Year:  Dec 2010/ Jan. 2011
Year or Semester: Third year/ Fifth Semester
Paper Code: 5E3257

Unit-I
1. Consider a system whose output y(n) is related to the input x(n) by y(n)= summision upto k=-infinity to + inifinity x(k) x(n+k).
Deter mine whether or not the system is
a)      Linear,
b)      Shift-inveriant,
c)       Stable
d)      Causal                                   [Marks 16]
OR
2. Consider a system described by the difference equation y(n)=y(n-1)-y(n-2)+0.5x(n)+0.5x(n-1) Find the response of this system to the input x(n)=(0.5)^n u(n) with initial conditions y(-1)=0.75 and y(-2)=0.25  [Marks 16]
Unit-II
3.  a) Prove the convolution theorem of DTFT. [Marks 8]
    b) Find the inverse DTFT of X(e^be)= 1/ (1-1/3 e^-f10w)                               [Marks 8]
OR
4. a) Find the Z-transform of x(n)=|n| (1/2) ^|n| [Marks 8]
    b) Find the inverse Z-transform of the second order system.
     X(Z)=(1+1/4 Z^-1) / (1-1/2 Z^-1)^2,  |Z|>2                                            [Marks 8]
Unit-III
5. Define and prove the sampling theorem. [Marks  16]
OR
6. Suppose that Xa(t) is band limited to 8KHz (that is, Xa(f)=0 for |f|>8000Hz).
i)                    What is the Nyquist rate for Xa(t)?
ii)                   What is the Nyquist rate for Xa(t) cos (2Pi 1000t)?     [Marks 8+8=16]
Unit-IV
7. Explain overlap add and overlap save method for computing linear convolution using DFT for longer input sequence x(n).                 [Marks 16]
OR
8. Derive radix 2 decimation in fre3quency FFT algorithm for evaluating 8 point DFT. [Marks 16]
Unit-V

9. Consider the causal linear shift invariant filter with system function
H(Z)=(1+0.875Z^-1)/ (1+0.2Z^-1+0.9Z^-2)(1-0.7 Z^-1)
Draw a signal flow graph for this system using.
i)                    Direct form-I              [Marks 2]
ii)                   Direct form-II             [Marks 2]
iii)                 A cascade of first and second order system realized in direct form II [Marks 4]
iv)                 A cascade of first and second order system realized in transposed direct form II [Marks 4]
v)                  A parallel connection of first and second order system realized in direct form II [Marks 4]
OR
10. Use the window design method to design a linear phase FIR filter of order N=24 to approximate the following ideal frequency response magnitude:
|Hd(e hx)|= 1   |w|<=0.2pi
                        0  0.2pi<|w|<=Pi

Unit-I
Consider a system whose output y(n) is related to the input x(n) by y(n)= summision upto k=-infinity to + inifinity x(k) x(n+k).
Deter mine whether or not the system is
a)      Linear,
b)      Shift-inveriant,
c)       Stable
d)      Causal                                   [Marks 16]
OR
2. Consider a system described by the difference equation y(n)=y(n-1)-y(n-2)+0.5x(n)+0.5x(n-1) Find the response of this system to the input x(n)=(0.5)^n u(n) with initial conditions y(-1)=0.75 and y(-2)=0.25  [Marks 16]
Unit-II
a) Prove the convolution theorem of DTFT. [Marks 8]
b) Find the inverse DTFT of X(e^be)= 1/ (1-1/3 e^-f10w)                               [Marks 8]
OR
a) Find the Z-transform of x(n)=|n| (1/2) ^|n| [Marks 8]
b) Find the inverse Z-transform of the second order system.
X(Z)=(1+1/4 Z^-1) / (1-1/2 Z^-1)^2,  |Z|>2                                            [Marks 8]
Unit-III
Define and prove the sampling theorem. [Marks  16]
OR
 Suppose that Xa(t) is band limited to 8KHz (that is, Xa(f)=0 for |f|>8000Hz).
i)                    What is the Nyquist rate for Xa(t)?
ii)                   What is the Nyquist rate for Xa(t) cos (2Pi 1000t)?     [Marks 8+8=16]
Unit-IV
7. Explain overlap add and overlap save method for computing linear convolution using DFT for longer input sequence x(n).                 [Marks 16]
OR
8. Derive radix 2 decimation in fre3quency FFT algorithm for evaluating 8 point DFT. [Marks 16]
Unit-V

9. Consider the causal linear shift invariant filter with system function
H(Z)=(1+0.875Z^-1)/ (1+0.2Z^-1+0.9Z^-2)(1-0.7 Z^-1)
Draw a signal flow graph for this system using.
i)                    Direct form-I              [Marks 2]
ii)                   Direct form-II             [Marks 2]
iii)                 A cascade of first and second order system realized in direct form II [Marks 4]
iv)                 A cascade of first and second order system realized in transposed direct form II [Marks 4]
v)                  A parallel connection of first and second order system realized in direct form II [Marks 4]
OR
10. Use the window design method to design a linear phase FIR filter of order N=24 to approximate the following ideal frequency response magnitude:
|Hd(e hx)|= 1   |w|<=0.2pi
                        0  0.2pi<|w|<=Pi
Unit-I
Consider a system whose output y(n) is related to the input x(n) by y(n)= summision upto k=-infinity to + inifinity x(k) x(n+k).
Deter mine whether or not the system is
a)      Linear,
b)      Shift-inveriant,
c)       Stable
d)      Causal                                   [Marks 16]
OR
2. Consider a system described by the difference equation y(n)=y(n-1)-y(n-2)+0.5x(n)+0.5x(n-1) Find the response of this system to the input x(n)=(0.5)^n u(n) with initial conditions y(-1)=0.75 and y(-2)=0.25  [Marks 16]
Unit-II
a) Prove the convolution theorem of DTFT. [Marks 8]
b) Find the inverse DTFT of X(e^be)= 1/ (1-1/3 e^-f10w)                               [Marks 8]
OR
a) Find the Z-transform of x(n)=|n| (1/2) ^|n| [Marks 8]
b) Find the inverse Z-transform of the second order system.
X(Z)=(1+1/4 Z^-1) / (1-1/2 Z^-1)^2,  |Z|>2                                            [Marks 8]
Unit-III
Define and prove the sampling theorem. [Marks  16]
OR
 Suppose that Xa(t) is band limited to 8KHz (that is, Xa(f)=0 for |f|>8000Hz).
i)                    What is the Nyquist rate for Xa(t)?
ii)                   What is the Nyquist rate for Xa(t) cos (2Pi 1000t)?     [Marks 8+8=16]
Unit-IV
7. Explain overlap add and overlap save method for computing linear convolution using DFT for longer input sequence x(n).                 [Marks 16]
OR
8. Derive radix 2 decimation in fre3quency FFT algorithm for evaluating 8 point DFT. [Marks 16]
Unit-V

9. Consider the causal linear shift invariant filter with system function
H(Z)=(1+0.875Z^-1)/ (1+0.2Z^-1+0.9Z^-2)(1-0.7 Z^-1)
Draw a signal flow graph for this system using.
i)                    Direct form-I              [Marks 2]
ii)                   Direct form-II             [Marks 2]
iii)                 A cascade of first and second order system realized in direct form II [Marks 4]
iv)                 A cascade of first and second order system realized in transposed direct form II [Marks 4]
v)                  A parallel connection of first and second order system realized in direct form II [Marks 4]
OR
10. Use the window design method to design a linear phase FIR filter of order N=24 to approximate the following ideal frequency response magnitude:
|Hd(e hx)|= 1   |w|<=0.2pi
                        0  0.2pi<|w|<=Pi
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